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Titlebook: Brownian Motion, Martingales, and Stochastic Calculus; Jean-François Le Gall Textbook 2016 Springer International Publishing Switzerland 2

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发表于 2025-3-21 19:42:00 | 显示全部楼层 |阅读模式
期刊全称Brownian Motion, Martingales, and Stochastic Calculus
影响因子2023Jean-François Le Gall
视频video
发行地址Provides a concise and rigorous presentation of stochastic integration and stochastic calculus for continuous semimartingales.Presents major applications of stochastic calculus to Brownian motion and
学科分类Graduate Texts in Mathematics
图书封面Titlebook: Brownian Motion, Martingales, and Stochastic Calculus;  Jean-François Le Gall Textbook 2016 Springer International Publishing Switzerland 2
影响因子This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter..Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. .Brownian Motion, Martingales, and Stochastic Calculus. provides astrong theoretical background to the reader interested in such developments..Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on co
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Scripture and Theological Method,ablish the conformal invariance of planar Brownian motion as a simple corollary of the results of Chap. . An important application is the so-called skew-product decomposition of planar Brownian motion, which we use to derive several asymptotic laws, including the celebrated Spitzer theorem on Brownian windings.
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Brownian Motion and Partial Differential Equations,ablish the conformal invariance of planar Brownian motion as a simple corollary of the results of Chap. . An important application is the so-called skew-product decomposition of planar Brownian motion, which we use to derive several asymptotic laws, including the celebrated Spitzer theorem on Brownian windings.
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0072-5285 applications of stochastic calculus to Brownian motion and This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the op
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Selma and the Voting Rights Act of 1965, property of continuity of sample paths, which is derived here via the classical Kolmogorov lemma. The end of the chapter discusses several properties of Brownian sample paths, and establishes the strong Markov property, with its classical application to the reflection principle.
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A New Direction: Chicago, 1966,. In a second step, we develop the theory of continuous time martingales, and, in particular, we derive regularity results for sample paths of martingales. We finally discuss the optional stopping theorem for martingales and supermartingales, and we give applications to explicit calculations of distributions related to Brownian motion.
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