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Review: Diffusions, Markov Processes, and Martingales: Volume 1, FoundationsUser Review - Joecolelife - Goodreads
This book, the first in a two volume set, is a wonderful survey of some of the most important results in modern mathematics. The books begin with Brownian motion, review results from measure theory ... Read full review
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a-algebra adapted process apply Borel Brownian bridge Brownian motion calculus canonical construct continuous local martingale continuous semimartingale coordinates deduce define definition denote density diffeomorphism differential equation Doleans dual previsible projection example excursion theory Exercise exponential filtration finite variation finite-variation follows function Hence increasing process independent inequality interval Ito's formula IV0 process Kunita Lemma Lie group Lipschitz Malliavin calculus manifold Markov process Markov property martingale null martingale problem matrix metric Meyer decomposition Moreover nonnegative notation obvious optional projection orthogonal orthonormal path pathwise uniqueness PCHAF Poisson Poisson process previsible stopping proof of Theorem prove R-process random variable Remarks result Riemannian right-continuous satisfies semimartingale sequence smooth space Stieltjes integral stochastic differential stochastic integral Stratonovich strong Markov property submartingale supermartingale Suppose Tanaka's formula tangent vector Theorem uniformly integrable uniformly integrable martingale uniqueness in law vector fields weak solution
Page 453 - Nonlinear Filtering and Stochastic Mechanics', in Stochastic Systems: The Mathematics of Filtering and Identification and
Page 456 - A local time analysis of intersections of Brownian paths in the plane, Ann.
Page 456 - Pitman (1980). Fluctuation identities for Levy processes and splitting at the maximum. Adv. Appl. Probab. 12 PE Greenwood and JW Pitman (1980-a).
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singularities), and these are fully discussed. In the opposite ...
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