扩散过程和偏微分方程
2005-4
世界图书出版公司
author
452
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本书是根据作者在Sophia大学、Hokkaido大学、Tohoku大学、Tokyo Metropolitan大学和Tsukuba大学的讲义整理而成，主旨是系统介绍概率论中马尔可夫过程构造问题的现代分析方法，即将马尔可夫过程的构造归结为研究二阶退化椭圆微分方程的的边值问题。为此本书详细介绍诸如：可测函数与函数空间、广义函数、策分流形、拟微分算子、退化椭圆微分方程的极值原理、椭圆边界问题，Feller半群等现代分析中基本内容与研究方法，最后介绍将这些理论与方法应用于马尔可夫过程构造问题。这是一部分析概率与偏微分程方面的优秀专著。
Preface Acknowledgments Notation and Conventions Iatroduetion and Summary Ⅰ Markov Processes and Semigroups Ⅱ Propagation of Maximums Ⅲ Construction of Feller Semigroups Chapter1 Preparatory Material 1.1 Sets 1.2 Mappings 1.3 Topological Spaces 1.4 Compactness 1.5 Connectedness 1.6 Metric Spaces 1.7 Baire‘s Category Theorem 1.8 Continuous Mappings 1.9 Linear Spaces 1.10 Linear Topological Spaces 1.11 Factor Spaces 1.12 Algebras and Modules 1.13 Linear Operators 1.14 Differentiable Mappings 1.15 Vector Fields and Integral Cuives 1.16 Measurable Spaces 1.17 Measurable Functions 1.18 Measures 1.19 Integrals 1.20 Probability Spaces NotesChapter2 Manifolds,Tensors and Densicties 2.1 Manifolds 2.2 C Mappings 2.3 Tangent Bundles 2.4 Vector Fields 2.5 Integral Curves 2.6 Cotangent Bundles 2.7 Tensors 2.8 Tensor Fields 2.9 Exterior Product 2.10 Differential Forms 2.11 Densities 2.12 Integration on Manifolds 2.13 Manifolds With Boundary NotesChapter3 Functional Analysis 3.1 Quasinormed Linear Spaces 3.2 Normed Linear Spaces 3.3 The Riesz Representation Theorem 3.4 Closed Operators 3.5 Complemented Subspaces 3.6 Compact Operators 3.7 Fredholm Operators 3.8 Hilbert Spaces 3.9 Theory 9of Semigroups NotesChapter4 Distributions,Operators and Kernels 4.1 Notation ……Chapter5 Sobolev SpacesChapter6 The Claculus of Pseudo-Differential OperatorsChapter7 Maximum Principles for Degenerate Elliptic OperatorsChapter8 Elliptic Boundary Value ProblemsChapter9 Markov Processes,Semigroups and Boundary Value ProblemsChapter10 Construction of Feller SemigroupsBibliographyList of SymbolsIndex
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