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Girsanov Theorem

Chapter
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Part of the Indian Statistical Institute Series book series (INSIS)

Abstract

In this chapter, we will obtain Girsanov Theorem and its generalizations by Meyer. Let M be a martingale on \((\varOmega ,{\mathcal F},{\mathsf{P}})\) and let \({\mathsf{Q}}\) be another probability measure on \((\varOmega ,{\mathcal F})\), absolutely continuous w.r.t. \({\mathsf{P}}\). Then as noted in Remark  4.26, M is a semimartingale on \((\varOmega ,{\mathcal F},{\mathsf{Q}})\). We will obtain a decomposition of M into N and B, where N is a \({\mathsf{Q}}\)-martingale. This result for Brownian motion was due to Girsanov, and we will also present the generalizations due to Meyer.

Keywords

Girsanov Theorem Absolute Continuity Semimartingale Brownian Motion Cameron-Martin Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Chennai Mathematical InstituteSiruseriIndia

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