Stochastic PDEs and Dynamics
by Boling Guo, Hongjun Gao, Xueke Pu
This book introduces the mathematics behind stochastic PDEs and their dynamical behavior. Starting with probability theory and stochastic processes, the authors discuss stochastic integrals, Itô's formula and Ornstein-Uhlenbeck processes, and they
Hardcover
English
Brand New
Publisher Description
This book explains mathematical theories of a collection of stochastic partial differential equations and their dynamical behaviors. Based on probability and stochastic process, the authors discuss stochastic integrals, Ito formula and Ornstein-Uhlenbeck processes, and introduce theoretical framework for random attractors. With rigorous mathematical deduction, the book is an essential reference to mathematicians and physicists in nonlinear science.Contents:PreliminariesThe stochastic integral and Itô formulaOU processes and SDEsRandom attractorsApplicationsBibliographyIndex
Author Biography
Boling Guo, Inst. of Applied Physics & Computational Maths;Hongjun Gao, Nanjing Normal Univ.;Xueke Pu, Chongqing Univ., China.
Table of Contents
Table of Content:Chapter 1 Preliminaries1.1 Preliminaries in probability1.2 Preliminaries of stochastic process1.3 Martingale1.4 Wiener process and Brown motion1.5 Poisson process1.6 Levy process1.7 The fractional Brownian motionChapter 2 The stochastic integral and Ito formula2.1 Stochastic integral2.2 Ito formula2.3 The infnite dimensional case2.4 Nuclear operator and Hilbert-Schmidt operatorChapter 3 OU processes and SDEs3.1 Ornstein-Uhlenbeck processes3.2 Linear SDEs3.3 Nonlinear SDEsChapter 4 Random attractors4.1 Determinate nonautonomous systems4.2 Stochastic dynamical systemsChapter 5 Applications5.1 Stochastic Ginzburg-Landau equation5.2 Ergodicity for SGL with degenerate noise5.3 Stochastic damped forced Ostrovsky equation5.4 Simplifed quasi geostrophic model5.5 Stochastic primitive equationsReferences
Long Description
This book explains mathematical theories of a collection of stochastic partial differential equations and their dynamical behaviors. Based on probability and stochastic process, the authors discuss stochastic integrals, Ito formula and Ornstein-Uhlenbeck processes, and introduce theoretical framework for random attractors. With rigorous mathematical deduction, the book is an essential reference to mathematicians and physicists in nonlinear science. Contents: Preliminaries The stochastic integral and It
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