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內(nèi)容簡介

　　本書是根據(jù)作者在Sophia大學、Hokkaido大學、Tohoku大學、Tokyo Metropolitan大學和Tsukuba大學的講義整理而成，主旨是系統(tǒng)介紹概率論中馬爾可夫過程構(gòu)造問題的現(xiàn)代分析方法，即將馬爾可夫過程的構(gòu)造歸結(jié)為研究二階退化橢圓微分方程的的邊值問題。為此本書詳細介紹諸如：可測函數(shù)與函數(shù)空間、廣義函數(shù)、策分流形、擬微分算子、退化橢圓微分方程的極值原理、橢圓邊界問題，F(xiàn)eller半群等現(xiàn)代分析中基本內(nèi)容與研究方法，最后介紹將這些理論與方法應用于馬爾可夫過程構(gòu)造問題。這是一部分析概率與偏微分程方面的優(yōu)秀專著。

作者簡介

暫缺《擴散過程和偏微分方程：英文版》作者簡介

圖書目錄

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