Boling Guo, Hongjun Gao, Xueke Pu

Stochastic PDEs and Dynamics (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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:
Preliminaries
The stochastic integral and Itô formula
OU processes and SDEs
Random attractors
Applications
Bibliography
Index

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Produktdetails

• Verlag: de Gruyter Oldenbourg
• Seitenzahl: 228
• Erscheinungstermin: 21. November 2016
• Englisch
• ISBN-13: 9783110492439
• Artikelnr.: 47449024

Autorenporträt

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

Inhaltsangabe

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