Derjaguin approximation: Difference between revisions

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{{Orphan|date=August 2013}}
I'm a 43 years old and study at the college (Nutritional Sciences).<br>In my spare time I try to learn Portuguese. I've been  there and look forward to go there sometime near future. I like to read, [http://Www.preferably.net/ preferably] on my beloved Kindle. I really love to watch Arrested Development and Arrested Development as well as documentaries about nature. I love Leaf collecting and pressing.<br><br>my blog post - discount exhibit trade show booth display; [http://www.affordabledisplays.com/products/338-Waveline-10ft-Fabric-Graphic-Backwall/815-10ft-wide-Waveline-Curved-Tension-Fabric-Graphic-Display---Kit-4/ www.affordabledisplays.com],
 
In [[mathematics]], the '''Chung–Fuchs theorem''', named after [[Wolfgang Heinrich Johannes Fuchs]] and [[Chung Kai-lai]], states that for a particle undergoing a [[random walk]] in m-dimensions, it is certain to come back infinitely often to any neighborhood of the origin on a one-dimensional line (m = 1) or two-dimensional plane (m = 2), but in three or more dimensional spaces it will leave to infinity.
 
Specifically, if a position of the particle is described by the vector <math>X_n</math>:
 
<math>X_n = Z_1 + ... + Z_n</math>
 
where <math>Z_1, Z_2, ... , Z_n</math> are independent m-dimensional vectors with a given multivariate distribution,
 
then if <math>m=1</math>, <math>E(|Z_i|) < \infty</math> and <math>E(Z_i)=0 </math>, or if <math>m=2</math> <math>E(|Z^2_i|) < \infty</math> and <math>E(Z_i)=0 </math>,
 
the following holds:
 
<math>\forall \epsilon>0</math>, <math>P(\forall n_0\ge 0, \exist n\ge n_0, |X_n| < \epsilon ) = 1</math>
 
However, for <math> m \ge  3</math>,
 
<math>\forall A>0</math>, <math>P(\exist n_0\ge0, \forall n\ge n_0, |X_n| \ge A) = 1</math>.
 
==References==
*{{Citation |last=Cox, Miller |title=The theory of stochastic processes |location=London |publisher=Chapman and Hall Ltd |year=1963}}.
 
* "On the distribution of values of sums of random variables" Chung, K.L. and Fuchs, W.H.J. Mem. Amer. Math. Soc. 1951 no.6, 12pp
 
{{DEFAULTSORT:Chung-Fuchs theorem}}
[[Category:Physics theorems]]

Latest revision as of 11:51, 5 May 2014

I'm a 43 years old and study at the college (Nutritional Sciences).
In my spare time I try to learn Portuguese. I've been there and look forward to go there sometime near future. I like to read, preferably on my beloved Kindle. I really love to watch Arrested Development and Arrested Development as well as documentaries about nature. I love Leaf collecting and pressing.

my blog post - discount exhibit trade show booth display; www.affordabledisplays.com,

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