多维扩散过程

图书标准信息

• 作者 Daniel、S.R.S.Varadhan 著
• 出版社 世界图书出版公司
• 出版时间 2009-03
• 版次 1
• ISBN 9787506292627
• 定价 55.00元
• 装帧 平装
• 开本 16开
• 纸张 其他
• 页数 338页
• 正文语种 英语

【内容简介】

　　《多维扩散过程》为英文版本，内容讲述了多维物体的扩散过程，讲解详细，易懂。

【目录】

FrequentlyUsedNotation
Chapter0Introduction
Chapter1PreliminaryMaterial：ExtensionTheorems，Martingales，andCompactness
1．0Introduction
1．1WeakConvergence．ConditionalProbabilityDistributionsandExtensionTheorems
1．2Martingales．
1．3TheSpacec([0，0)；R)
1．4MartingalesandCompactness
1．5Exercises

Chapter2MarkovProcesses，RegularityofTheirSamplePaths，andtheWienerMeasure．
2．1RegularityofPaths
2．2MarkOVProcessesandTransitionProbabilities
2．3WienerMeasure
2．4Exercises

Chapter3ParabolicPartialDifferentialEquations
3．1TheMaximumPrinciple．
3．2ExistenceTheorems
3．3Exercises

Chapter4TheStochasticCalculusofDi斤usionTheory
4．1BrownianMorion，
4．2EquivalenceofCertainMartingales
4．3It6ProcessesandStochasticIntegration
4．4It’sFormula
4．5ItProcessesasStochasticIntegrals
4．6ExerciSes

Chapter5StochasticDilierentialEquations
5．0Introduction
5．1ExistenceandUniqueness
5．2OntheLipschitzCondition
5．3EquivalenceofDifferentChoicesoftheSquareRoot
5．4Exercises

Chapter6TheMartingaleFormulation
6．0Introduction
6．1Existence
6．2Uniqueness：MarkovProperty
6．3Uniqueness：SomeExamples．
6．4Cameron．Martin．GirsanovFormula
6．5Uniqueness：RandomTimeChange
6．6Uniqueness：Localization．
6．7Exercises

Chapter7Uniqueness
7．0Introduction
7．1Uniqueness：LocalCase
7．2Uniqueness：GlobalCase
7．3ExereiSes

Chapter8It’SUniquenessandUniquenesstotheMartingaleProblem
8．0Introduction．
8．IResultsofYamadaandWatanabe
8．2More0nItbUniqueness
8．3Exercises

Chapter9SomeEstimatesontheTransitionProbabilityFunctions
9．0Introduetion
9．1TheInhomogeneousCase
9．2TheHomogeneousCase

Chapter10Explosion
10．0Introduction
10．1LocallyBoundedCocfficients
10．2ConditionsforExplosionandNon-Explosion
10．3Exercises．

Chapter11LimitTheorems
11．0Introduction
11．1ConvergenceofDiffusionProcess
11．2ConvergenceofMarkovChainstoDiffusions
11．3ConvergenceofDiffusionProcesses：EllipticCase
11．4ConvergenceofTransitionProbabilityDensities
11．5ExerciSeS

Chapter12TheNon—UniqueCase
12．0Introduction
12．1ExistenceofMeasurableChoices
12．2MarkovSelections
12．3ReconstructionofAllSolutions
12．4Exercises

Appendix
A．0Introduction
A．1LEstimatesforSomeSingularIntegralOperators
A．2ProofoftheMainEstimate
A．3Exercises
BibliographicalRemarks
Bibliography
Index