Guo, B: Stochastic PDEs and Dynamics
Beschreibung:
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.
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 It formulaOU processes and SDEsRandom attractorsApplicationsBibliographyIndex
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