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| | A tenancy-in-frequent agreement is used each time there may be frequent possession of a property. A person might opt for real estate investment with his siblings, friends, or every other celebration. In any of those instances, this can be a good option. It describes how the property is owned and what is the duty of each proprietor. That is one of the simplest ways to divide the property with none issues.<br><br>JLL ranked high actual estate funding advisor in Asia Pacific Newest information from Actual Capital Analytics (RCA) exhibits real property advisory agency advised on probably the most deals by worth within the area in 2013 JLL named Greatest Performing Property Brand for second year [http://mattleibius.buzznet.com/user/journal/18235691/commercial-industrial-launch/ http://mattleibius.buzznet.com] running JLL has been named Greatest Performing Property Model at the 12th Annual MPF Awards for Administration Excellence. Through its wholly-ownded subsidiary, Frasers Centrepoint Restricted ("FCL"), Fraser and Neave, Limited ("F&N") has a world portfolio of high quality residential properties, serviced residences, actual property and fund administration, and industrial properties which embrace retail malls, workplaces and business parks. FCL is one in all Singapore's high three property corporations with total property of over $8 billion.<br><br>Sebastian Skiff, Govt Director for CBRE Retail Asia, seems on a section filmed in Hong Kong for Bloomberg TV's In the Loop with Betty Liu, giving her a tour of Causeway Bay outlets. FROM BLOOMBERG TELEVISION The current climate of low rates of interest, globally and in Singapore, is likely to persist for a while. It's going to continue to spur demand within the residential property market, pushing up prices beyond sustainable levels. The eventual correction could possibly be painful to debtors and destabilise the economy. The new MAS rules impose an absolute limit of 35 years on the tenure of all loans for residential property. This can apply to loans to each individual and non-particular person debtors, in addition to refinancing loans 1 , from 6 October 2012. 2 CLASH OF CULTURES<br><br>The Infocomm Development Authority of Singapore (IDA) provides assist within the info-communications points. GPS Company leasing manages corporations'relocation requirement and supply a one cease answer for corporations' personnel finding in Singapore ranging from CEO to executives. It includes of professionally trained full time employed staffs to ensure the purchasers relocation in Singapore is seamless and problem free. Extra Investment Gross sales Department b) Singapore Permanent Residents (PR) who already personal 1 or more residential properties, whether or not owned wholly, partially, or jointly with others c) Singapore Citizens (SC) who already own 2 or extra residential properties, whether or not owned wholly, partially, or collectively with others Private property<br><br>Jerry, your patients and non-pushy style is why we selected you over others. Well Performed and Thank You for recommending such a stunning house to us"<br><br>The brokers say that many Chinese language buyers are additionally investing overseas so they can own property close to main instructional institutions. Some are shopping for houses near prime colleges — even though their children are so little they can't stroll but. More than eighty percent of rich Chinese wish to ship their children overseas to high school, in accordance with the Hurun Report, a Shanghai-primarily based publication. Chinese language patrons typically used to choose up properties within the $1 to $5 million range in New York, often buying two and three at a time for funding functions, the brokers stated. Monika Tu, a broker at prime-end real property firm Black Diamondz Property Concierge in Sydney, says that over the past yr mainland Chinese language have change into 80 percent of her firm's enterprise. WCEGA Plaza & Tower<br><br>This web site is visited by many Singapore property hunters EVERYDAY! My objective is to draw native & abroad consumers who're considering shopping for Singapore properties & real estates. I am dedicated to offering high quality service to all my shoppers. And with my native & abroad database, I am at all times eager to tell & replace my patrons on the latest and best purchase properties and real estates in Singapore. Simply simply name me or replenish my ( Selling / Leasing Enquiry ) form when you're able to put up your property on the market.Your property will receive its personal net web page which incorporates full property info and images, links to maps, community information and / or streaming video & Virtual Tours. |
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| In [[probability]] and [[statistics]], a '''factorial moment measure''' is a [[mathematical]] quantity, [[Function (mathematics)|function]] or, more precisely, [[Measure (mathematics)|measure]] that is defined in relation to [[mathematical objects]] known as [[point process]]es, which are types of [[stochastic processes]] often used as [[mathematical model]]s of physical phenomena representable as [[random]]ly positioned [[Point (geometry)|points]] in [[time]],[[space]] or both. Moment measures generalize the idea of [[factorial moment]]s, which are useful for studying [[non-negative]] [[integer]]-valued [[random variables]].<ref name="daleyPPI2003">D. J. Daley and D. Vere-Jones. ''An introduction to the theory of point processes. Vol. I''. Probability and its Applications (New York). Springer, New York, second edition, 2003.
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| </ref>
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| The first factorial moment measure of a point process coincides with its [[Moment_measure#First_moment_measure|first moment measure]] or ''intensity measure'',<ref name="BB1">F. Baccelli and B. Błaszczyszyn. ''Stochastic Geometry and Wireless Networks, Volume I – Theory'', volume 3, No 3-4 of ''Foundations and Trends in Networking''. NoW Publishers, 2009.
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| </ref> which gives the [[Expected value|expected]] or [[average]] number of points of the point process located in some region of space. In general, if the number of points in some region is considered as a random variable, then the moment factorial measure of this region is the factorial moment of this random variable.<ref name="stoyan1995stochastic">D. Stoyan, W. S. Kendall, J. Mecke, and L. Ruschendorf. ''Stochastic geometry and its applications'', volume 2. Wiley Chichester, 1995.</ref> Factorial moment measures completely characterize a wide class of point processes, which means they can be used to uniquely identify a point process.
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| If a factorial moment measure is [[absolutely continuous]], then with respect to the [[Lebesgue measure]] it is said to have a ''density'' (which is a generalized form of a [[derivative]]), and this density is known by a number of names including '''factorial moment density''', '''product density''', '''coincidence density''',<ref name="daleyPPI2003"/> '''joint intensity'''<ref name="hough2006determinantal">{{cite journal| author=Hough, J Ben, Krishnapur, Manjunath, Peres, Yuval, Vir{\'a}g, B{\'a}lint| title=Determinantal processes and independence| journal=Probability Surveys| year=2006| volume=3| pages=206–229| accessdate=6 November 2013}}</ref>
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| , '''correlation function''' or '''multivariate frequency spectrum''' <ref name="handa2009two">K. Handa. The two-parameter {Poisson-Dirichlet} point process. ''Bernoulli'', 15(4):1082–1116, 2009.
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| </ref> The first and second factorial moment densities of a point process are used in the defintion of the ''pair correlation function'', which gives a way to statistically quantify the strength of interaction or [[correlation]] between points of a point process.<ref name="baddeley2007spatial">A. Baddeley, I. B{\'a}r{\'a}ny, and R. Schneider. Spatial point processes and their applications. ''Stochastic Geometry: Lectures given at the CIME Summer School held in Martina Franca, Italy, September 13–18, 2004'', pages 1–75, 2007.
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| </ref> | |
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| Factorial moment measures serve as useful tools in the study of point processes<ref name="daleyPPI2003"/><ref name="baddeley2007spatial"/><ref name="daleyPPII2008">D. J. Daley and D. Vere-Jones. ''An introduction to the theory of point processes. Vol. {II''}. Probability and its Applications (New York). Springer, New York, second edition, 2008</ref> as well as the related fields of [[stochastic geometry]]<ref name="stoyan1995stochastic"/> and [[spatial statistics]],<ref name="baddeley2007spatial"/><ref name="moller2003statistical">J. Moller and R. P. Waagepetersen. ''Statistical inference and simulation for spatial point processes''. CRC Press, 2003.</ref> which are applied in various [[scientific]] and [[engineering]] disciplines such as [[biology]], [[geology]], [[physics]], and [[telecommunications]].<ref name="daleyPPI2003"/><ref name="stoyan1995stochastic"/><ref name="BB2">F. Baccelli and B. Błaszczyszyn. ''Stochastic Geometry and Wireless Networks, Volume II – Applications'', volume 4, No 1-2 of ''[[Foundations and Trends in Networking]]''. NoW Publishers, 2009.</ref>
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| ==Point process notation==
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| {{Main|Point process notation}}
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| Point processes are mathematical objects that are defined on some underlying [[mathematical space]]. Since these processes are often used to represent collections of points randomly scattered in space, time or both, the underlying space is usually ''d''-dimensional [[Euclidean space]] denoted here by '''R'''<sup>d</sup>, but they can be defined on more [[Abstraction (mathematics)|abstract]] mathematical spaces.<ref name="daleyPPII2008"/>
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| Point processes have a number of interpretations, which is reflected by the various types of [[point process notation]].<ref name="stoyan1995stochastic"/><ref name="BB2">F. Baccelli and B. Błaszczyszyn. ''Stochastic Geometry and Wireless Networks, Volume II – Applications'', volume 4, No 1–2 of ''Foundations and Trends in Networking''. NoW Publishers, 2009.
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| </ref> For example, if a point <math>\textstyle x</math> belongs to or is a member of a point process, denoted by ''N'', then this can be written as:<ref name="stoyan1995stochastic"/>
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| : <math>\textstyle x\in {N},</math>
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| and represents the point process being interpreted as a random [[Set (mathematics)|set]]. Alternatively, the number of points of ''N'' located in some [[Borel set]] ''B'' is often written as:<ref name="BB1"/><ref name="stoyan1995stochastic"/><ref name="moller2003statistical">{{cite doi|10.1201/9780203496930}}</ref>
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| : <math>\textstyle {N}(B), </math>
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| which reflects a [[random measure]] interpretation for point processes. These two notations are often used in parallel or interchangeably.<ref name="stoyan1995stochastic"/><ref name="moller2003statistical"/><ref name="BB1">{{cite doi|10.1561/1300000006}}</ref>
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| ==Definitions==
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| ===''n'' th factorial power of a point process===
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| For some positive [[integer]] <math>\textstyle n=1,2,\dots</math>, the <math>\textstyle n</math>-th factorial power of a point process <math>\textstyle {N}</math> on <math>\textstyle \textbf{R}^d</math> is defined as:<ref name="BB1"/>
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| :<math> {N}^{(n)}(B_1\times,\dots,\times B_n)= \sum_{(x_1\neq,\dots,\neq x_n)\in {N} } \prod_{i=1}^n \mathbf{1}_{B_i}(x_i) </math>
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| where <math>\textstyle B_1,...,B_n</math> is a collection of not necessarily [[Disjoint sets|disjoint]] Borel sets in <math>\textstyle \textbf{R}^d</math>, which form a <math>\textstyle n</math>-fold [[Cartesian product]] of sets denoted by:
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| :<math> B_1\times,\dots,\times B_n.</math>
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| The symbol <math>\textstyle \mathbf{1}</math> denotes an [[indicator function]] such that <math>\textstyle \mathbf{1}_{B_1} </math>is a [[Dirac measure]] for the set <math>\textstyle B_n</math>. The [[summation]] in the above expression is performed over all <math>\textstyle n</math>-[[tuples]] of distinct points, including [[permutations]], which can be contrasted with the definition of the [[Moment measure#n-th power of a point process|''n''-th power of a point process]]. The symbol <math>\textstyle \Pi</math> denotes [[multiplication#Capital Pi notation|multiplication]] while the existence of various [[point process notation]] means that the ''n''-th factorial power of a point process is sometimes defined using other notation.<ref name="BB1"/> | |
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| ===''n'' th factorial moment measure===
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| The ''n'' th factorial moment measure or ''n'' th order factorial moment measure is defined as:
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| :<math> M^{(n)}(B_1\times,\dots,\times B_n)=E [{N}^{(n)}(B_1\times,\dots,\times B_n)], </math>
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| where the ''E'' denotes the [[Expected value|expectation]] ([[Operator (mathematics)#Probability theory|operator]]) of the point process ''N''. In other words, the ''n''-th factorial moment measure is the expectation of the ''n'' th factorial power of some point process.
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| The ''n'' th factorial moment measure of a point process ''N'' is equivalently defined<ref name="stoyan1995stochastic"/> by: | |
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| :<math> \int_{\textbf{R}^{n d}}f(x_1,\dots,x_n) M^{(n)}(dx_1,\dots,dx_n)=E \left[ \sum_{(x_1\neq,\dots,\neq x_n)\in {N} } f(x_1,\dots,x_n) \right], </math>
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| where ''f'' is any non-negative [[measurable function]] on '''R'''<sup>nd</sup>, and the above summation is performed over all ''n'' tuples of distinct points, including permutations. Consequently, the factorial moment measure is defined such that there are no points repeating in the product set, as opposed to the moment measure.<ref name="daleyPPII2008"/>
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| ===First factorial moment measure===
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| The first factorial moment measure <math>\textstyle M^1</math> coincides with the [[Moment measure#First moment measure|first moment measure]]:<ref name="BB1"/>
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| :<math> M^{(1)}(B)=M^1(B)=E [{N}(B)], </math>
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| where <math>\textstyle M^1</math> is known, among other terms, as the ''intensity measure''<ref name="stoyan1995stochastic"/> or ''mean measure'',<ref name="kingman1992poisson">J. F. C. Kingman. ''Poisson processes'', volume 3. Oxford university press, 1992.
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| </ref> and is interpreted as the expected number of points of <math>\textstyle {N}</math> found or located in the set <math>\textstyle B</math>
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| ===Second factorial moment measure===
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| The second factorial moment measure for two Borel sets <math>\textstyle A</math> and <math>\textstyle B</math> is:
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| :<math> M^{(2)}(A\times B)=M^1(A\times B)-M^1(A\cap B). </math>
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| ==Name explanation==
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| For some Borel set <math>\textstyle B</math>, the namesake of this measure is revealed when the <math>\textstyle n\,</math>th factorial moment measure reduces to:
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| :<math> M^{(n)}(B\times,\dots,\times B)=E [{N}(B)({N}(B)-1)\dots ({N}(B)-n+1)], </math>
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| which is the <math>\textstyle n\,</math>-th [[factorial moment]] of the random variable <math>\textstyle {N}(B)</math>.<ref name="stoyan1995stochastic"/>
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| ==Factorial moment density==
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| If a factorial moment measure is [[absolutely continuous]], then it has a density (or more precisely, a [[Radon–Nikodym derivative]] or density) with respect to the [[Lebesgue measure]] and this density is known as the ''factorial moment density'' or ''product density'', ''joint intensity'', ''correlation function'', or ''multivariate frequency spectrum''. Denoting the <math>\textstyle n</math>-th factorial moment density by <math>\textstyle \mu^{(n)}(x_1,\dots,x_n)</math>, it is defined in respect to the equation:<ref name="stoyan1995stochastic"/>
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| :<math> M^{(n)}(B_1\times,\dots,\times B_n)=\int_{B_1}\dots\int_{B_n}\mu^{(n)}(x_1,\dots,x_n) dx_1\dots dx_n. </math>
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| Furthermore, this means the following expression
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| :<math> E \left[ \sum_{(x_1\neq,\dots,\neq x_n)\in {N} } f(x_1,\dots,x_n) \right]= \int_{\textbf{R}^{n d}} f(x_1,\dots,x_n) \mu^{(n)}(x_1,\dots,x_n) dx_1\dots dx_n, </math>
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| where <math>\textstyle f</math> is any non-negative [[Bounded function|bounded]] measurable function defined on <math>\textstyle \textbf{R}^{ n}</math>.
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| ==Pair correlation function==
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| In spatial statistics and stochastic geometry, to measure the statistical [[Correlation and dependence|correlation]] relationship between points of a point process, the ''pair correlation function'' of a point process <math>{N}</math> is defined as:<ref name="stoyan1995stochastic"/><ref name="baddeley2007spatial"/>
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| :<math> \rho(x_1,x_2)=\frac{\mu^{(2)}(x_1,x_2)}{\mu^{(1)}(x_1) \mu^{(1)}(x_2) }, </math>
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| where the points <math>x_1,x_2\in R^d </math>. In general, <math>\rho(x_1,x_2)\geq 0</math> whereas <math>\rho(x_1,x_2)=1</math> corresponds to no correlation (between points) in the typical statistical sense.<ref name="baddeley2007spatial"/>
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| ==Examples==
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| ===Poisson point process===
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| For a [[general Poisson point process]] with intensity measure <math>\textstyle \Lambda</math> the <math>\textstyle n</math>-th factorial moment measure is given by the expression:<ref name="stoyan1995stochastic"/>
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| :<math> M^{(n)}(B_1\times,\dots,\times B_n)=\prod_{i=1}^n[\Lambda(B_i)], </math>
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| where <math>\textstyle \Lambda</math> is the intensity measure or first moment measure of <math>\textstyle {N}</math>, which for some Borel set <math>\textstyle B</math> is given by:
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| :<math> \Lambda(B)=M^1(B)=E[{N}(B)]. </math>
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| For a [[homogeneous Poisson point process]] the <math>\textstyle n</math>-th factorial moment measure is simply:<ref name="BB1"/>
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| :<math> M^{(n)}(B_1\times,\dots,\times B_n)=\lambda^n \prod_{i=1}^n |B_i|, </math>
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| where <math>\textstyle |B_i|</math> is the length, area, or volume (or more generally, the [[Lebesgue measure]]) of <math>\textstyle B_i</math>. Furthermore, the <math>\textstyle n</math>-th factorial moment density is:<ref name="stoyan1995stochastic"/>
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| :<math> \mu^{(n)}(x_1,\dots,x_n)=\lambda^n. </math>
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| The pair-correlation function of the homogeneous Poisson point process is simply
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| :<math> \rho(x_1,x_2)=1, </math>
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| which reflects the lack of interaction between points of this point process.
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| ==Factorial moment expansion==
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| It has been shown that expectations of general [[Functional (mathematics)|functional]]s of simple point processes, provided some [[Convergence (mathematics)|convergence]] condition, have (possibly infinite) expansions or [[Series (mathematics)|series]] consisting of the corresponding factorial moment measures.<ref name="fme">B. Blaszczyszyn. Factorial-moment expansion for stochastic systems. ''Stoch. Proc. Appl.'', 56:321–335, 1995.
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| </ref><ref name="fme_marked">D. P. Kroese and V. Schmidt. Light-traffic analysis for queues with spatially distributed arrivals. ''Mathematics of Operations Research'', 21(1):pp. 135–157, 1996. | |
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| </ref> In comparison to the [[Taylor series]], which consists of a series of [[derivative]]s of some function, the ''n''th factorial moment measure plays the roll as that of the ''n'' th derivative the Taylor series. In other words, given a general functional ''f'' of some simple point process, then this [[Taylor's theorem|Taylor-like theorem]] for non-Poisson point processes means an expansion exists for the expectation of the function ''E'', provided some mathematical condition is satisfied, which ensures convergence of the expansion.
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| ==See also==
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| * [[Factorial moment]]
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| * [[Moment (mathematics)|Moment]]
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| * [[Moment measure]]
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| ==References==
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| {{notelist}}
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| <references/>
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| [[Category:Probability theory]]
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| [[Category:Spatial data analysis]]
| |
A tenancy-in-frequent agreement is used each time there may be frequent possession of a property. A person might opt for real estate investment with his siblings, friends, or every other celebration. In any of those instances, this can be a good option. It describes how the property is owned and what is the duty of each proprietor. That is one of the simplest ways to divide the property with none issues.
JLL ranked high actual estate funding advisor in Asia Pacific Newest information from Actual Capital Analytics (RCA) exhibits real property advisory agency advised on probably the most deals by worth within the area in 2013 JLL named Greatest Performing Property Brand for second year http://mattleibius.buzznet.com running JLL has been named Greatest Performing Property Model at the 12th Annual MPF Awards for Administration Excellence. Through its wholly-ownded subsidiary, Frasers Centrepoint Restricted ("FCL"), Fraser and Neave, Limited ("F&N") has a world portfolio of high quality residential properties, serviced residences, actual property and fund administration, and industrial properties which embrace retail malls, workplaces and business parks. FCL is one in all Singapore's high three property corporations with total property of over $8 billion.
Sebastian Skiff, Govt Director for CBRE Retail Asia, seems on a section filmed in Hong Kong for Bloomberg TV's In the Loop with Betty Liu, giving her a tour of Causeway Bay outlets. FROM BLOOMBERG TELEVISION The current climate of low rates of interest, globally and in Singapore, is likely to persist for a while. It's going to continue to spur demand within the residential property market, pushing up prices beyond sustainable levels. The eventual correction could possibly be painful to debtors and destabilise the economy. The new MAS rules impose an absolute limit of 35 years on the tenure of all loans for residential property. This can apply to loans to each individual and non-particular person debtors, in addition to refinancing loans 1 , from 6 October 2012. 2 CLASH OF CULTURES
The Infocomm Development Authority of Singapore (IDA) provides assist within the info-communications points. GPS Company leasing manages corporations'relocation requirement and supply a one cease answer for corporations' personnel finding in Singapore ranging from CEO to executives. It includes of professionally trained full time employed staffs to ensure the purchasers relocation in Singapore is seamless and problem free. Extra Investment Gross sales Department b) Singapore Permanent Residents (PR) who already personal 1 or more residential properties, whether or not owned wholly, partially, or jointly with others c) Singapore Citizens (SC) who already own 2 or extra residential properties, whether or not owned wholly, partially, or collectively with others Private property
Jerry, your patients and non-pushy style is why we selected you over others. Well Performed and Thank You for recommending such a stunning house to us"
The brokers say that many Chinese language buyers are additionally investing overseas so they can own property close to main instructional institutions. Some are shopping for houses near prime colleges — even though their children are so little they can't stroll but. More than eighty percent of rich Chinese wish to ship their children overseas to high school, in accordance with the Hurun Report, a Shanghai-primarily based publication. Chinese language patrons typically used to choose up properties within the $1 to $5 million range in New York, often buying two and three at a time for funding functions, the brokers stated. Monika Tu, a broker at prime-end real property firm Black Diamondz Property Concierge in Sydney, says that over the past yr mainland Chinese language have change into 80 percent of her firm's enterprise. WCEGA Plaza & Tower
This web site is visited by many Singapore property hunters EVERYDAY! My objective is to draw native & abroad consumers who're considering shopping for Singapore properties & real estates. I am dedicated to offering high quality service to all my shoppers. And with my native & abroad database, I am at all times eager to tell & replace my patrons on the latest and best purchase properties and real estates in Singapore. Simply simply name me or replenish my ( Selling / Leasing Enquiry ) form when you're able to put up your property on the market.Your property will receive its personal net web page which incorporates full property info and images, links to maps, community information and / or streaming video & Virtual Tours.