Stochastic PDEs and Dynamics

Boling Guo, Inst. of Applied Physics & Computational Maths;Hongjun Gao, Nanjing Normal Univ.;Xueke Pu, Chongqing Univ., China.

• 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