纯粹数学与应用数学专著:随机动力系统导论(英文)
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110
8.6折
¥
128
九品
库存2件
作者段金桥 著
出版社科学出版社
出版时间2015-01
版次1
装帧平装
上书时间2024-08-22
商品详情
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图书标准信息
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作者
段金桥 著
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出版社
科学出版社
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出版时间
2015-01
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版次
1
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ISBN
9787030438577
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定价
128.00元
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装帧
平装
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开本
16开
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纸张
胶版纸
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页数
283页
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正文语种
英语
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丛书
纯粹数学与应用数学专著
- 【内容简介】
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随机动力系统是一个入门较难的新兴领域。
《纯粹数学与应用数学专著:随机动力系统导论(英文)》是这个领域的一个较为通俗易懂的引论。
在《纯粹数学与应用数学专著:随机动力系统导论(英文)》的第一部分,作者从简单的随机动力系统实际例子出发,引导读者回顾概率论和白噪声的基本知识,深入浅出地介绍随机微积分,然后自然地展开随机微分方程的讨论。
- 【目录】
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Chapter1Introduction
1.1Examplesofdeterministicdynamicalsystems
1.2Examplesofstochasticdynamicalsystems
1.3Mathematicalmodelingwithstochasticdifferentialequations
1.4Outlineofthisbook
1.5Problems
Chapter2BackgroundinAnalysisandProbability
2.1Euclideanspace
2.2Hilbert,Banachandmetricspaces
2.3Taylorexpansions
2.4ImproperintegralsandCauchyprincipalvalues
2.5Someusefulinequalities
2.5.1Young'sinequality
2.5.2Cronwallinequality
2.5.3Cauchy-Schwaxzinequality
2.5.4HSlderinequality
2.5.5Minkowskiinequality
2.6HSlderspaces,Sobolevspacesandrelatedinequalities
2.7Probabilityspaces
2.7.1Scalarrandomvariables
2.7.2Randomvectors
2.7.3Gaussianrandomvariables
2.7.4Non-Gaussianrandomvariables
2.8Stochasticprocesses
2.9Coovergenceconcepts
2.10Simulation
2.11Problems
Chapter3Noise
3.1Brownianmotion
3.1.1BrownianmotioninR1
3.1.2BrownianmotioninRn~
3.2WhatisGaussianwhitenoise
3.3*AmathematicalmodelforGaussianwhitenoise
3.3.1Generalizedderivatives
3.3.2Gaussianwhitenoise
3.4Simulation
3.5Problems
Chapter4ACrashCourseinStochasticDifferentialEquations
4.1Differentialequationswithnoise
4.2Riemann-Stieltjesintegration
4.3Stochasticintegrationandstochasticdifferentialequations
4.3.1Motivation
4.3.2DefinitionofIt5integral
4.3.3Practicalcalculations
4.3.4Stratonovichintegral
4.3.5Examples
4.3.6PropertiesofIt6integrals
4.3.7Stochasticdifferentialequations
4.3.8SDEsinengineeringandscienceliterature
4.3.9SDEswithtwo-sidedBrownianmotions
4.4It'sformula
4.4.1MotivationforstochasticChainrules
4.4.2ItS'sformulainscalarcase
4.4.3It6'sformulainvectorcase
4.4.4Stochasticproductruleandintegrationbyparts
4.5Linearstochasticdifferentialequations
4.6Nonlinearstochasticdifferentialequations
4.6.1Existence,uniquenessandsmoothness
4.6.2ProbabilitymeasurepxandexpectationExassociatedwithanSDE
4.7ConversionbetweenIt5andStratonovichstochasticdifferentialequations
4.7.1ScalarSDEs
4.7.2SDEsystems
4.8Impactofnoiseondynamics
4.9Simulation
4.10Problems
Chapter5DeterministicQuantitiesforStochasticDynamics
5.1Moments
5.2Probabilitydensityfunctions
5.2.1ScalarFokker-Planckequations
5.2.2MultidimensionalFokker-Planckequations
5.2.3ExistenceanduniquenessforFokker-Planckequations
5.2.4Likelihoodfortransitionsbetweendifferentdynamicalregimesunderuncertainty
5.3Mostprobablephaseportraits
5.3.1Meanphaseportraits
5.3.2Almostsurephaseportraits
5.3.3Mostprobablephaseportraits
5.4Meanexittime
5.5Escapeprobability
5.6Problems
Chapter6InvariantStructuresforStochasticDynamics
6.1Deterministicdynamicalsystems
6.1.1Conceptsfordeterministicdynamicalsystems
6.1.2TheHaxtman-Grobmantheorem
6.1.3Invariantsets
6.1.4Differentiablemanifolds
6.1.5Deterministicinvariantmanifolds
6.2Measurabledynamicalsystems
6.3Randomdynamicalsystems
6.3.1CanonicalsamplespacesforSDEs
6.3.2Wienershift
6.3.3Cocyclesandrandomdynamicalsystems
6.3.4Examplesofcocycles
6.3.5Structuralstabilityandstationaryorbits
6.4Linearstochasticdynamics
6.4.1Oseledets'multiplicativeergodictheoremandLyapunovexponents"
6.4.2AstochasticHartman-Grobmantheorem
6.5*Randominvariantmanifolds
6.5.1Definitionofrandominvariantmanifolds
6.5.2ConvertingSDEstoRDEs
6.5.3Localrandompseudo-stableandpseudo-unstablemanifolds
6.5.4Localrandomstable,unstableandcentermanifolds
6.6Problems
Chapter7DynamicalSystemsDrivenbyNon-GaussianLevyMotions
7.1ModelingviastochasticdifferentialequationswithLevymotions
7.2Levymotions
7.2.1Functionsthathaveone-sidelimits
7.2.2Levy-Itodecomposition
7.2.3Levy-Khintchineformula
7.2.4BasicpropertiesofLevymotions
7.3s-stableLevymotions
7.3.1Stablerandomvariables
7.3.2a-stableLevymotionsinR1
7.3.3a-stableLevymotioninRn
7.4StochasticdifferentialequationswithLevymotions
7.4.1StochasticintegrationwithrespecttoLevymotions
7.4.2SDEswithLevymotions
7.4.3GeneratorsforSDEswithLevymotion
7.5Meanexittime
7.5.1Meanexittimefora-stableLevymotion
7.5.2MeanexittimeforSDEswitha-stableLevymotion
7.6Escapeprobabilityandtransitionphenomena
7.6.1Balayage-Dirichletproblemforescapeprobability
7.6.2Escapeprobabilityfora-stableLevymotion
7.6.3EscapeprobabilityforSDEswitha-stableLevymotion
7.7Fokker-Planckequations
7.7.1Fokker-PlanckequationsinR1
7.7.2Fokker-PlanckequationsinRn
7.8Problems
HintsandSolutions
FurtherReadings
References
Index
ColorPictures
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