扩散过程和偏微分方程：英文版

　　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。

暂缺《扩散过程和偏微分方程：英文版》作者简介

Preface
Acknowledgments
NotationandConventions
IatroduetionandSummary
IMarkovProcessesandSemigroups
IIPropagationofMaximums
IIIConstructionofFellerSemigroups
Chapter1PreparatoryMaterial
1.1Sets
1.2Mappings
1.3TopologicalSpaces
1.4Compactness
1.5Connectedness
1.6MetricSpaces
1.7Baire'sCategoryTheorem
1.8ContinuousMappings
1.9LinearSpaces
1.10LinearTopologicalSpaces
1.11FactorSpaces
1.12AlgebrasandModules
1.13LinearOperators
1.14DifferentiableMappings
1.15VectorFieldsandIntegralCurves
1.16MeasurableSpaces
1.17MeasurableFunctions
1.18Measures
1.19Integrals
1.20ProbabilitySpaces
Notes
Chapter2Manifolds,TensorsandDensities
2.1Manifolds
2.2CMappings
2.3TangentBundles
2.4VectorFields
2.5IntegralCurves
2.6CotangentBundles
2.7Tensors
2.8TensorFields
2.9ExteriorProduct
2.10DifferentialForms
2.11Densities
2.12IntegrationonManifolds
2.13ManifoldswithBoundary
Notes
Chapter3FunctionalAnalysis
3.1QuasinormedLinearSpaces
3.2NormedLinearSpaces
3.3TheRieszRepresentationTheorem
3.4ClosedOperators
3.5ComplementedSubspaces
3.6CompactOperators
3.7FredholmOperators
3.8HilbertSpaces
3.9TheoryofSemigroups
Notes
Chapter4Distributions,OperatorsandKernels
4.1Notation
4.2FunctionSpaces
4.3DifferentialOperators
4.4Distributions
4.5OperatorsandKernels
4.6DistributionsonaManifold
4.7DifferentialOperatorsonaManifold
4.8OperatorsandKernelsonaManifold
4.9DomainsofClassCr
4.10TheSee]eyExtensionTheorem
Notes
Chapter5SobolevSpaces
5.1TheSpacesHs(Rn)
5.2TheSpacesHsloc(Ω)
5.3TheSpacesHs(M)
5.4TheSpacesHs(Rn+)
5.5TheSpacesHs(Ω)
5.6TraceTheorems
5.7SobolevSpacesandRegularizations
Notes
Chapter6TheCalculusofPseudo-DifferentialOperators
6.1SymbolClasses
6.2PhaseFunctions
6.3OscillatoryIntegrals
6.4FourierIntegralOperators
6.5Pseudo-DifferentialOperators
6.6Pseudo-DifferentialOperatorsonaManifold
6.7EllipticPseudo-DifferentialOperatorsandtheirIndices
6.8PotentialsandPseudo-DifferentialOperators
6.9TheSharpGardingInequality
6.10HypoellipticPseudo-DifferentialOperators
Notes
Chapter7MaximumPrinciplesforDegenerateEllipticOperators
7.1MaximumPrinciples
7.2PropagationofMaximums
Notes
Chapter8EllipticBoundaryValueProblems
8.1TheDirichletProblem--(1)--
8.2TheDirichletProblem--(2)--
8.3GeneralBoundaryValueProblems
8.4ExistenceandUniquenessTheoremforGeneralBoundary
ValueProblems
Notes
Chapter9MarkovProcesses,SemigroupsandBoundaryValue
Problems
9.1MarkovProcessesandTransitionFunctions
9.2TransitionFunctionsandFellerSemigroups
9.3FellerSemigroupsandtheirInfinitesimalGenerators
9.4InfinitesimalGeneratorsofFellerSemigroups--(1)--
9.5InfinitesimalGeneratorsofFellerSemigroups--(2)--
9.6FellerSemigroupsandBoundaryValueProblems
Notes
Chapter10ConstructionofFellerSemigroups
10.1StatementofResults
10.2ProofofTheorem10.1.1
10.3ProofofTheorem10.1.3
Notes
Bibliography
ListofSymbols
Index