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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Novikov's condition ： ウィキペディア英語版 Novikov's condition 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 $(X\_t)\_$ is a real valued adapted process on the probability space $\backslash left\; (\backslash Omega,\; (\backslash mathcal\_t),\; \backslash mathbb\backslash right)$ and $(W\_t)\_$ is an adapted Brownian motion:〔Pascucci, Andrea (2011) ''PDE and Martingale Methods in Option Pricing''. Berlin: Springer-Verlag〕 If the condition : $$ \mathbb\left( \right )<\infty is fulfilled then the process : $$ \ \mathcal\left( \int_0^t X_s \; dW_s \right) \ = e^\int_0^t X_s^2\, ds},\quad 0\leq t\leq T is a martingale under the probability measure $\backslash mathbb$ and the filtration $\backslash mathcal$. Here $\backslash mathcal$ denotes the Doléans-Dade exponential. ==References== Comments on Girsanov's Theorem by H. E. Krogstad, IMF 2003 () 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Novikov's condition」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.