Seminaire de Probabilites XXXV
J. Azema, M. Emery, M. Ledoux, M. Yor
Springer Science & Business Media, Apr 10, 2001 - Mathematics - 384 pages
Researchers and graduate students in the theory of stochastic processes will find in this 35th volume some thirty articles on martingale theory, martingales and finance, analytical inequalities and semigroups, stochastic differential equations, functionals of Brownian motion and of LÚvy processes. Ledoux's article contains a self-contained introduction to the use of semigroups in spectral gaps and logarithmic Sobolev inequalities; the contribution by Emery and Schachermayer includes an exposition for probabilists of Vershik's theory of backward discrete filtrations.
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adapted apply assume bounded Brownian motion compact condition Consequently consider constant construction continuous convergence Corollary d'une defined definition denote density depending diffusion distribution equal equivalent example exists extension fact filtration finie finite fixed formula function given gives Hence holds hypothesis immersed implies independent instant integrable Lemma limit locale logarithmic Sobolev inequalities martingale Mathematics measure non-atomic Notes obtain operator particular positive predictable premier previsible Probabilites probability problem proof Proposition prove random variables recall References relation Remark representation respect result satisfies sauts semimartingale sequence simple solution space Springer standard stochastic stochastic differential equations structure sufficient suite Suppose surely taking temps term Theorem Theory tout transform uniform uniformly unique values variation verify