Continuous Martingales and Brownian Motion
From the reviews: "This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion. The great strength of Revuz and Yor is the enormous variety of calculations carried out both in the main text and also (by implication) in the exercises. ... This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises, and throwing out challenging remarks about areas awaiting further research..."
Bull.L.M.S. 24, 4 (1992) Since the first edition in 1991, an impressive variety of advances has been made in relation to the material of this book, and these are reflected in the successive editions.
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adapted apply associated Borel function bounded Brownian motion called Chap compact complete compute condition consequently consider constant continuous local martingale converges Corollary defined Definition denote density derivative distribution easily equal equation equivalent example Exercise exists extended fact filtration finite follows formula function function f further Gaussian give given hence Hint holds important increasing independent inequality integrable interval invariant Lemma limit linear BM Markov process Markov property Moreover namely notation observe obtained pair particular paths positive predictable probability measure proof Proposition prove question random reader Remark respect result right-continuous satisfies scaling Sect seen semi-group semimartingale sequence shows solution space standard stochastic differential equation stochastic integral stopping strictly strong taken taking Theorem transform uniformly unique values vanishing variables variation write zero
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Side 570 - Poisson point processes attached to Markov processes. Proc. Sixth Berkeley Symp. Math. Stat.
Side 566 - On the distribution of the Hilbert transform of the local time of a symmetric Levy process. Ann.