Description
Book SynopsisThis 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 Itô formula OU processes and SDEs Random attractors Applications Bibliography Index
Table of ContentsTable of Content: Chapter 1 Preliminaries 1.1 Preliminaries in probability 1.2 Preliminaries of stochastic process 1.3 Martingale 1.4 Wiener process and Brown motion 1.5 Poisson process 1.6 Levy process 1.7 The fractional Brownian motion Chapter 2 The stochastic integral and Ito formula 2.1 Stochastic integral 2.2 Ito formula 2.3 The infnite dimensional case 2.4 Nuclear operator and Hilbert-Schmidt operator Chapter 3 OU processes and SDEs 3.1 Ornstein-Uhlenbeck processes 3.2 Linear SDEs 3.3 Nonlinear SDEs Chapter 4 Random attractors 4.1 Determinate nonautonomous systems 4.2 Stochastic dynamical systems Chapter 5 Applications 5.1 Stochastic Ginzburg-Landau equation 5.2 Ergodicity for SGL with degenerate noise 5.3 Stochastic damped forced Ostrovsky equation 5.4 Simplifed quasi geostrophic model 5.5 Stochastic primitive equations References
