連續鞅和布朗運動 下載 mobi epub pdf 電子書 2024

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　　每一部分的結束都有好多補充的練習題，一方麵這些習題可以很好的幫助讀者提高對這《連續鞅和布朗運動》中引入的新觀點的理解。另外一方麵這些練習也是對《連續鞅和布朗運動》內容的豐富和完備化。

內容簡介

　　《連續鞅和布朗運動》是一部很經典的講述隨機過程及布朗運動的教材（全英文版）。其旨在盡可能詳細的嚮概率專傢介紹盡可能多的有關布朗運動的觀點、技巧和方法。自從1991年這《連續鞅和布朗運動》的第一版本問世以來，有關布朗運動和相關的隨機過程一直是人們研究和討論的熱點。布朗運動是許多典型的概率問題連續鞅、高斯過程、馬爾科夫過程甚至更特殊的具有獨立增量的過程的交叉點。大量新的方法都能夠成功的應用於它的研究，新的版本也就應運而生。《連續鞅和布朗運動》在第一章引入布朗運動後，以後的各章都是具體在講述某一種特定的方法或者觀點。在這些方法中貫穿於《連續鞅和布朗運動》始終的是隨機積分以及強有力的遊程理論。

目錄

Chapter 0.Preliminaries
§1.Basic Notation
§2.Monotone Class Theorem
§3.Completion
§4.Functions of Finite Variation and Stieltjes Integrals
§5.Weak Convergence in Metric Spaces
§6.Gaussian and Other Random Variables

ChapterⅠ.Introduction
§1.Examples of Stochastic Processes.Brownian Motion
§2.Local Properties of Brownian Paths
§3.Canonical Processes and Gaussian Processes
§4.Filtrations and Stopping Times
Notes and Comments

ChapterⅡ.Martingales
§1.Definitions， Maximal Inequalities and Applications
§2.Convergence and Regularization Theorems
§3.Optional Stopping Theorem
Notes and Comments

ChapterⅢ.Markov Processes
§1.Basic Definitions
§2.Feller Processes
§3.Strong Markov Property
§4.Summary of Results on Levy Processes
Notes and Comments

ChapterⅣ.Stochastic Integration
§1.Quadratic Variations
§2.Stochastic Integrals
§3.Itos Formula and First Applications
§4.Burkholder-Davis-Gundy Inequalities
§5.Predictable Processes
Notes and Comments

ChapterⅤ.Representation of Martingales
§1.Continuous Martingales as Time-changed Brownian Motions
§2.Conformal Martingales and Planar Brownian Motion
§3.Brownian Martingales
§4.Integral Representations
Notes and Comments

ChapterⅥ.Local Times
§1.Definition and First Properties
§2.The Local Time of Brownian Motion
§3.The Three-Dimensional Bessel Process
§4.First Order Calculus
§5.The Skorokhod Stopping Problem
Notes and Comments

ChapterⅦ.Generators and Time Reversal
§1.Infinitesimal Generators.
§2.Diffusions and Ito Processes
§3.Linear Continuous Markov Processes
§4.Time Reversal and Applications
Notes and Comments

ChapterⅧ.Girsanovs Theorem and First Applications
§1.Girsanovs Theorem
§2.Application of Girsanovs Theorem to the Study of Wieners Space
§3.Functionals and Transformations of Diffusion Processes
Notes and Comments

ChapterⅨ.Stochastic Differential Equations
§1.Formal Definitions and Uniqueness
§2.Existence and Uniqueness in the Case of Lipschitz Coefficients
§3.The Case of Holder Coefficients in Dimension One
Notes and Comments

ChapterⅩ.Additive Functionals of Brownian Motion
§1.General Definitions
§2.Representation Theorem for Additive Functionals of Linear Brownian Motion
§3.Ergodic Theorems for Additive Functionals
§4.Asymptotic Results for the Planar Brownian Motion
Notes and Comments

ChapterⅪ.Bessel Processes and Ray-Knight Theorems
§1.Bessel Processes
§2.Ray-Knight Theorems
§3.Bessel Bridges
Notes and Comments

ChapterⅫ.Excursions
§1.Prerequisites on Poisson Point Processes
§2.The Excursion Process of Brownian Motion
§3.Excursions Straddling a Given Time
§4.Descriptions of Itos Measure and Applications
Notes and Comments

Chapter XIII.Limit Theorems in Distribution
§1.Convergence in Distribution
§2.Asymptotic Behavior of Additive Functionals of Brownian Motion
§3.Asymptotic Properties of Planar Brownian Motion

Notes and Comments
Appendix
§1.Gronwalls Lemma
§2.Distributions
§3.Convex Functions
§4.Hausdorff Measures and Dimension
§5.Ergodic Theory
§6.Probabilities on Function Spaces
§7.Bessel Functions
§8.Sturm-Liouville Equation

Bibliography
Index of Notation
Index of Terms
Catalogue

前言/序言

連續鞅和布朗運動 下載 mobi epub pdf txt 電子書 格式

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鞅的原名 martingale 原指一類於18世紀流行於法國的投注策略，稱為加倍賭注法（英語：Martingale (betting system)）。[1]這類策略中最簡單的一種策略是為博弈設計的。在博弈中，賭徒會擲硬幣，若硬幣正麵嚮上，賭徒會贏得賭本，若硬幣反麵嚮上，賭徒會輸掉賭本。這一策略使賭徒在輸錢後加倍賭金投注，為的是在初次贏錢時贏迴之前輸掉的所有錢，同時又能另外贏得與最初賭本等值的收益。當賭徒的財産和可用時間同時接近無窮時，他擲硬幣後硬幣正麵嚮上的概率會接近1，由此看來，加倍賭注法似乎是一種必然能贏錢的策略。然而，賭金的指數增長最終會導緻使用這一策略的賭徒破産。

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很經典的書

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連續鞅的經典教材，springer數學係列太強大瞭

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很經典的書

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