Stochastic Pdes and Dynamics

ISBN-13: 9783110495102 / Angielski / Twarda / 2016 / 228 str.

Boling Guo; Hongjun Gao; Xueke Pu

Opis

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 introduce the theoretical framework of random attractors. The rigorous presentation of the contents makes this book an essential reference for mathematicians and physicists alike.

Spis treści

Table 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

O autorze

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