<電子ブック>
Continuous Martingales and Brownian Motion

責任表示
著者
本文言語
出版者
出版年
出版地
関連情報
概要 This book focuses on the probabilistic theory ofBrownian motion. This is a good topic to center a discussion around because Brownian motion is in the intersec tioll of many fundamental classes of proc...esses. It is a continuous martingale, a Gaussian process, a Markov process or more specifically a process with in dependent increments; it can actually be defined, up to simple transformations, as the real-valued, centered process with independent increments and continuous paths. It is therefore no surprise that a vast array of techniques may be success fully applied to its study and we, consequently, chose to organize the book in the following way. After a first chapter where Brownian motion is introduced, each of the following ones is devoted to a new technique or notion and to some of its applications to Brownian motion. Among these techniques, two are of para mount importance: stochastic calculus, the use ofwhich pervades the whole book and the powerful excursion theory, both of which are introduced in a self contained fashion and with a minimum of apparatus. They have made much easier the proofs of many results found in the epoch-making book of Itö and McKean: Diffusion Processes and their Sampie Paths, Springer (1965).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
Index of Notation
Index of Terms.
続きを見る
本文を見る Full text available from SpringerLink ebooks - Mathematics and Statistics (Archive)

詳細

レコードID
主題
SSID
eISBN
登録日 2020.06.27
更新日 2020.06.28