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 process additive functional almost-surely Bessel processes Brownian Bridge Brownian motion cadlag called Chap compact completes the proof compute condition consequently constant cont continuous local martingale continuous semimartingale converges in distribution Corollary countable defined Definition denote density derivative equal equation equivalent excursion Exercise exists exponential Feller process filtration finite variation follows function f Girsanov's theorem given hence Hint independent inequality infinity interval invariant Ito's formula Lebesgue measure Lemma Levy processes locally bounded Markov process Markov property mart Moreover notation oo a.s. particular Poisson process positive Borel function predictable process Prob probability measure probability space Proposition prove random variables reader real number Remark resp respect result right-continuous Sect semi-group semimartingale sequence solution standard linear BM stochastic integral stopping strictly positive strong Markov property submartingale subset Tanaka's formula time-change uniformly integrable unique vanishing zero
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Page 570 - Poisson point processes attached to Markov processes. Proc. Sixth Berkeley Symp. Math. Stat.
Page 566 - On the distribution of the Hilbert transform of the local time of a symmetric Levy process. Ann.
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