| 词条 | 随机微分方程 |
| 释义 | 图书信息书名：随机微分方程 出版社: 世界图书出管社; 第1版 (2006年11月1日) 平装: 365页 开本: 24开 isbn: 750627308x 条形码: 9787506273084 商品尺寸: 22.5 x 15 x 1.6 cm 商品重量: 422 g 品牌: 世界图书出版公司北京公司 内容简介《随机微分方程》(第6版)是《Universitext》丛书之一，是一部理想的研究生教材，内容做了较大的修改和补充，包括鞅表示论、变分不等式和随机控制等内容，书后附有部分习题解答和提示。随机微分方程在数学以外的许多领域有着广泛的应用，它对数学领域中的许多分支起着有效的联结作用。 作者简介作者：(挪)科森多尔 目录Introduction 1.1 Stochastic Analogs of Classical Differential Equations 1.2 Filtering Problems 1.3 Stochastic Approach to Deterministic Boundary Value Problems 1.4 Optimal Stopping 1.5 Stochastic Control 1.6 Mathematical Finance Some Mathematical Preliminaries 2.1 Probability Spaces, Random Variables and Stochastic Processes 2.2 An Important Example: Brownian Motion Exercises Ito Integrals 3.1 Construction of the It5 Integral 3.2 Some properties of the It5 integral 3.3 Extensions of the Ito integral Exercises The Ito Formula and the Martingale Representation Theorem 4.1 The 1-dimensional It5 formula 4.2 The Multi-dimensional It5 Formula 4.3 The Martingale Representation Theorem Exercises Stochastic Differential Equations 5.1 Examples and Some Solution Methods 5.2 An Existence and Uniqueness Result 5.3 Weak and Strong Solutions Exercises 6 The Filtering Problem 6.1 Introduction 6.2 The 1-Dimensional Linear Filtering Problem 6.3 The Multidimensional Linear Filtering Problem Exercises 7 Diffusions: Basic Properties 7.1 The Markov Property 7.2 The Strong Markov Property 7.3 The Generator of an It5 Diffusion 7.4 The Dynkin Formula 7.5 The Characteristic Operator Exercises 8 Other Topics in Diffusion Theory 8.1 Kolmogorov's Backward Equation. The Resolvent 8.2 The Feynman-Kac Formula. Killing 8.3 The Martingale Problem 8.4 When is an It5 Process a Diffusion? 8.5 Random Time Change 8.6 The Girsanov Theorem Exercises 9 Applications to Boundary Value Problems 9.1 The Combined Dirichlet-Poisson Problem. Uniqueness 9.2 The Dirichlet Problem. Regular Points 9.3 The Poisson Problem Exercises 10 Application to Optimal Stopping 10.1 The Time-Homogeneous Case 10.2 The Time-Inhomogeneous Case 10.3 Optimal Stopping Problems Involving an Integral 10.4 Connection with Variational Inequalities Exercises 11 Application to Stochastic Control 11.1 Statement of the Problem 11.2 The Ha.milton-Jacobi-Bellman Equation 11.3 Stochastic control problems with terminal conditions Exercises 12 Application to Mathematical Finance 12.1 Market, portfolio and arbitrage 12.2 Attainability and Completeness 12.3 Option Pricing Exercises Appendix A: Normal Random Variables Appendix B: Conditional Expectation Appendix C: Uniform Integrability and Martingale Convergence Appendix D: An Approximation Result Solutions and Additional Hints to Some of the Exercises.. References List of Frequently Used Notation and Symbols Index |
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