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內容簡介

　　《隨機積分導論（第2版）（英文版）》是一部可讀性很強的講述隨機積分和隨機微分方程的入門教程。將基本理論和應用巧妙結閤，非常適閤學習過概率論知識的研究生，學習隨機積分。運用現代方法，隨機積分的定義是為瞭可料被積函數和局部鞅，緊接著是連續鞅的變分公式ito變化。《隨機積分導論（第2版）（英文版）》包括在布朗運動的描述、鞅的hermite多項式、feynman-kac泛函和schrodinger方程。這是第二版，討論瞭cameron-martin-giranov變換，並且在最後一章引入隨機微分方程和一些學生用的練習。

內頁插圖

目錄

Preface
Preface to the First Edition
Abbreviations and Symbols
1. Preliminaries
1.1 Notations And Conventions
1.2 Measurability, Lp Spaces And Monotone Class Theorems
1.3 Functions of Bounded Variation And Stieltjes Integrals
1.4 Probability Space, Random Variables, Filtration
1.5 Convergence, Conditioning
1.6 Stochastic Processes
1.7 Optional Times
1.8 Two Canonical Processes
1.9 Martingales
1.10 Local Martingales
1.11 Exercises

2. Definition of The Stochastic Integral
2.1 Introduction
2.2 Predictable Sets And Processes
2.3 Stochastic Intervals
2.4 Measure on The Predictable Sets
2.5 Definition of The Stochastic Integral
2.6 Extension To Local Integrators And Integrands
2.7 Substitution Formula
2.8 A Sufficient Condition for Extendability of Hz
2.9 Exercises

3. Extension of The Predictable Integrands
3.1 Introduction
3.2 Relationship Between P, O, And Adapted Processes
3.3 Extension of The Integrands
3.4 A Historical Note
3.5 Exercises

4. Quadratic Variation Process
4.1 Introduction
4.2 Definition And Characterization of Quadratic Variation
4.3 Properties of Quadratic Variation For An L2-Wartingale
4.4 Direct Definition of ΜM
4.5 Decomposition of （M）2
4.6 A Limit Theorem
4.7 Exercises

5. The Ito Formula
5.1 Introduction
5.2 One-Dimensional It5 Formula
5.3 Mutual Variation Process
5.4 Multi-Dimensional It5 Formula
5.5 Exercises
……
6. Applications of The Ito Formula
7. Local Time and Tanaka's Formula
8. Reflected Brownian Motions
9. Generalized Fro Formula,Change of Time and Measure
10. Stochastic Differential Equations

前言/序言

隨機積分導論（第2版，英文版） [Introduction to Stochastic Integration(Second Edition)] 下載 mobi epub pdf txt 電子書

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