Guo / Gao / Pu Stochastic PDEs and Dynamics

1. Auflage 2016
ISBN: 978-3-11-049243-9
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 228 Seiten

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

Zielgruppe

Graduate students and researchers in mathematics and physics.

Autoren/Hrsg.

Guo, Boling

Gao, Hongjun

Pu, Xueke

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

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

Über Autor(innen)

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