Milnor conjecture (topology)

In probability theory, Novikov's condition is the sufficient condition for a stochastic process which takes the form of the Radon-Nikodym derivative in Girsanov's theorem to be a martingale. If satisfied together with other conditions, Girsanov's theorem may be applied to a Brownian Motion stochastic process to change from the original measure to the new measure defined by the Radon-Nikodym derivative.

This condition was suggested and proved by Alexander Novikov. There are other results which may be used to show that the Radon-Nikodym derivative is a martingale, such as the more general criterion Kazamaki's condition, however Novikov's condition is the most well-known result.

Assume that $(X_t{)}_{0\le t\le T}$ is a real valued adapted process on the probability space $(\mathrm{\Omega },({\mathcal{ℱ}}_t),\mathbb{\mathbb{P}})$ and $(W_t{)}_{0\le t\le T}$ is an adapted Brownian motionPrimarily based on the most recent URA personal property value index (PPPI) flash estimates, we know that the PPPI, which represents the overall real property price development, has dipped in 2013Q4. That is the first dip the market has seen within the final 2 years.

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Within the event the Bank's valuation is decrease than the acquisition price, the purchaser has to pay the distinction between the purchase value and the Bank's valuation utilizing money. As such, the money required up-front might be increased so it's at all times essential to know the valuation of the property before making any offer. Appoint Lawyer The Bank will prepare for a proper valuation of the property by way of physical inspection The completion statement will present you the balance of the acquisition price that you must pay after deducting any deposit, pro-rated property tax and utility costs, upkeep prices, and different relevant expenses in addition to any fees payable to the agent and the lawyer. Stamp Responsibility Primarily based on the Purchase Price or Market Value, whichever is larger:

If the condition

$\mathbb{𝔼}\left[e^{\frac{1}{2}\underset{0}{\overset{T}{\int }}|X_t{|}^{2}dt}\right]<\mathrm{\infty }$

is fulfilled then the process

$Z_t=e^{\underset{0}{\overset{t}{\int }}{X}_{s}d{W}_s-\frac{1}{2}\underset{0}{\overset{t}{\int }}{X}_s^{2}ds},0\le t\le T$

is a martingale under the probability measure $\mathbb{\mathbb{P}}$ and the filtration $\mathcal{ℱ}$.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro. Comments on Girsanov's Theorem by H. E. Krogstad, IMF 2003[1]