随机微分方程-(第6版)
本书特色
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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。本书是《Universitext》丛书之一，是一部理想的研究生教材。我们曾影印出版了第2版和第4版，第6版与第4版相比，内容做了较大的修改和补充，增加了90页的篇幅(近1／3内容)，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。
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内容简介
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本书包括鞅表示论、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。
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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 FinanceSome Mathematical Preliminaries 2.1 Probability Spaces, Random Variables and Stochastic Processes 2.2 An Important Example: Brownian MotionExercisesIto Integrals 3.1 Construction of the It5 Integral 3.2 Some properties of the It5 integral 3.3 Extensions of the Ito integralExercisesThe Ito Formula and the Martingale RepresentationTheorem 4.1 The 1-dimensional It5 formula 4.2 The Multi-dimensional It5 Formula 4.3 The Martingale Representation TheoremExercisesStochastic Differential Equations 5.1 Examples and Some Solution Methods 5.2 An Existence and Uniqueness Result 5.3 Weak and Strong Solutions Exercises6 The Filtering Problem 6.1 Introduction 6.2 The 1-Dimensional Linear Filtering Problem 6.3 The Multidimensional Linear Filtering Problem Exercises7 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 Exercises8 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 Exercises9 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 Exercises10 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 Exercises11 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 Exercises12 Application to Mathematical Finance 12.1 Market, portfolio and arbitrage 12.2 Attainability and Completeness 12.3 Option Pricing ExercisesAppendix A: Normal Random VariablesAppendix B: Conditional ExpectationAppendix C: Uniform Integrability and Martingale ConvergenceAppendix D: An Approximation ResultSolutions and Additional Hints to Some of the Exercises..ReferencesList of Frequently Used Notation and SymbolsIndex
封面
书名:随机微分方程-(第6版)
作者:BERNTKSENDAL
页数:365
定价:¥39.0
出版社:世界图书出版公司
出版日期:2006-05-01
ISBN:9787506273084
PDF电子书大小:38MB 高清扫描完整版