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Continuous Martingales and Brownian Motion

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概要 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 motio...n. 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.続きを見る
目次 0. Preliminaries
I. Introduction
II. Martingales
III. Markov Processes
IV. Stochastic Integration
V. Representation of Martingales
VI. Local Times
VII. Generators and Time Reversal
VIII. Girsanov's Theorem and First Applications
IX. Stochastic Differential Equations
X. Additive Functionals of Brownian Motion
XI. Bessel Processes and Ray-Knight Theorems
XII. Excursions
XIII. Limit Theorems in Distribution
{sect}1. Gronwall's Lemma
{sect}2. Distributions
{sect}3. Convex Functions
{sect}4. Hausdorff Measures and Dimension
{sect}5. Ergodic Theory
{sect}6. Probabilities on Function Spaces
{sect}7. Bessel Functions
{sect}8. Sturm-Liouville Equation
Index of Notation
Index of Terms
Catalogue.
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登録日 2020.06.27
更新日 2020.06.28