Titlebook: Continuous Martingales and Brownian Motion; Daniel Revuz,Marc Yor Book 19911st edition Springer-Verlag Berlin Heidelberg 1991 Brownian mot

溫順

Integrate

https://doi.org/10.1007/978-3-322-83046-3In this chapter we study the effect on the space of continuous semimartingales of an absolutely continuous change of probability measure. The results we describe have far-reaching consequences from the theoretical point of view as is hinted at in Sect. 2; they also permit many explicit computations as is seen in Sect. 3.

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通知

Abduct

discord

Preliminaries,In this chapter, we review a few basic facts, mainly from integration and classical probability theories, which will be used throughout the book without further ado. Some other prerequisites, usually from calculus, which will be used in some special parts are collected in the Appendix at the end of the book.

淘氣

Martingales,Martingales are a very important subject in their own right as well as by their relationship with analysis. Their kinship to BM will make them one of our main subjects of interest as well as one of our foremost tools. In this chapter, we describe some of their basic properties which we shall use throughout the book.

枕墊

Representation of Martingales,In this chapter, we take up the study of Brownian motion and, more generally, of continuous martingales. We will use the stochastic integration of Chap. IV together with the technique of time changes to be introduced presently.

相符

Local Times,With It?’s formula, we saw how ..-functions operate on continuous semi-martingales. We now extend this to convex functions, thus introducing the important notion of local time.