000			06168cam a2200589Mi 4500
001			ocn872989896
003			OCoLC
005			20190328114807.0
006			m o d
007			cr |||||||||||
008			140224s2014 ne o 000 0 eng d
040			_aUKMGB _beng _erda _epn _cUKMGB _dOCLCO _dOPELS _dN$T _dE7B _dYDXCP _dOCLCQ _dOCLCF _dAU@ _dEBLCP _dIDEBK _dCOO _dDEBSZ _dOCLCQ _dDEBBG _dOCLCQ _dFEM _dITD _dMERUC _dOCLCQ _dBUF _dU3W _dD6H _dOTZ _dOCLCQ _dWYU _dTKN
016	7		_a016651344 _2Uk
019			_a874322618 _a880316058 _a880408011 _a968098901 _a969022648 _a1048424238
020			_a9780128012697 _q(electronic bk.)
020			_a0128012692 _q(electronic bk.)
020			_a1306737419 _q(ebk)
020			_a9781306737418 _q(ebk)
020			_a0128008822
020			_a9780128008829
020			_z9780128008829
035			_a(OCoLC)872989896 _z(OCoLC)874322618 _z(OCoLC)880316058 _z(OCoLC)880408011 _z(OCoLC)968098901 _z(OCoLC)969022648 _z(OCoLC)1048424238
050		4	_aQA274.25
072		7	_aMAT _x003000 _2bisacsh
072		7	_aMAT _x029000 _2bisacsh
082	0	4	_a519.2 _223
100	1		_aDuan, Jinqiao, _eauthor.
245	1	0	_aEffective dynamics of stochastic partial differential equations / _h[electronic resource] _cJinqiao Duan, Wei Wang.
264		1	_aAmsterdam : _bElsevier, _c2014.
300			_a1 online resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _2rda
490	0		_aElsevier insights
500			_aPreviously issued in print: 2014.
520			_aEffective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors' experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty. Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Solutions or hints to all Exercises.
588	0		_aCIP data; resource not viewed.
505	0		_aHalf Title; Title Page; Copyright; Dedication; Contents; Preface; 1 Introduction; 1.1 Motivation; 1.2 Examples of Stochastic Partial Differential Equations; 1.3 Outlines for This Book; 1.3.1 Chapter 2: Deterministic Partial Differential Equations; 1.3.2 Chapter 3: Stochastic Calculus in Hilbert Space; 1.3.3 Chapter 4: Stochastic Partial Differential Equations; 1.3.4 Chapter 5: Stochastic Averaging Principles; 1.3.5 Chapter 6: Slow Manifold Reduction; 1.3.6 Chapter 7: Stochastic Homogenization; 2 Deterministic Partial Differential Equations; 2.1 Fourier Series in Hilbert Space.
505	8		_a2.2 Solving Linear Partial Differential Equations2.3 Integral Equalities; 2.4 Differential and Integral Inequalities; 2.5 Sobolev Inequalities; 2.6 Some Nonlinear Partial Differential Equations; 2.6.1 A Class of Parabolic PDEs; 2.6.1.1 Outline of the Proof of Theorem 2.4; 2.6.2 A Class of Hyperbolic PDEs; 2.6.2.1 Outline of the Proof of Theorem 2.5; 2.7 Problems; 3 Stochastic Calculus in Hilbert Space; 3.1 Brownian Motion and White Noise in Euclidean Space; 3.1.1 White Noise in Euclidean Space; 3.2 Deterministic Calculus in Hilbert Space; 3.3 Random Variables in Hilbert Space.
505	8		_a3.4 Gaussian Random Variables in Hilbert Space3.5 Brownian Motion and White Noise in Hilbert Space; 3.5.1 White Noise in Hilbert Space; 3.6 Stochastic Calculus in Hilbert Space; 3.7 It�o's Formula in Hilbert Space; 3.8 Problems; 4 Stochastic Partial Differential Equations; 4.1 Basic Setup; 4.2 Strong and Weak Solutions; 4.3 Mild Solutions; 4.3.1 Mild Solutions of Nonautonomous spdes; 4.3.2 Mild Solutions of Autonomous spdes; 4.3.2.1 Formulation; 4.3.2.2 Well-Posedness Under Global Lipschitz Condition; 4.3.2.3 Well-Posedness Under Local Lipschitz Condition; 4.3.2.4 An Example.
505	8		_a4.4 Martingale Solutions4.5 Conversion Between It�o and Stratonovich SPDEs; 4.5.1 Case of Scalar Multiplicative Noise; 4.5.2 Case of General Multiplicative Noise; 4.5.3 Examples; 4.6 Linear Stochastic Partial Differential Equations; 4.6.1 Wave Equation with Additive Noise; 4.6.2 Heat Equation with Multiplicative Noise; 4.7 Effects of Noise on Solution Paths; 4.7.1 Stochastic Burgers' Equation; 4.7.2 Likelihood for Remaining Bounded; 4.8 Large Deviations for SPDEs; 4.9 Infinite Dimensional Stochastic Dynamics; 4.9.1 Basic Concepts; 4.9.2 More Dynamical Systems Concepts.
505	8		_a4.10 Random Dynamical Systems Defined by SPDEs4.10.1 Canonical Probability Space for SPDEs; 4.10.2 Perfection of Cocycles; 4.10.3 Examples; 4.11 Problems; 5 Stochastic Averaging Principles; 5.1 Classical Results on Averaging; 5.1.1 Averaging in Finite Dimension; 5.1.2 Averaging in Infinite Dimension; 5.2 An Averaging Principle for Slow-Fast SPDEs; 5.3 Proof of the Averaging Principle Theorem 5.20; 5.3.1 Some a priori Estimates; 5.3.2 Averaging as an Approximation; 5.4 A Normal Deviation Principle for Slow-Fast SPDEs; 5.5 Proof of the Normal Deviation Principle Theorem 5.34.
650		0	_aStochastic partial differential equations.
650		7	_aMATHEMATICS _xApplied. _2bisacsh
650		7	_aMATHEMATICS _xProbability & Statistics _xGeneral. _2bisacsh
650		7	_aStochastic partial differential equations. _2fast _0(OCoLC)fst01133516
655		4	_aElectronic books.
700	1		_aWang, Wei, _eauthor.
776	0	8	_iPrint version: _z9780128008829
856	4	0	_3ScienceDirect _uhttp://www.sciencedirect.com/science/book/9780128008829
999			_c246889 _d246889