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Stochastic PDEs and Dynamics de Boling Guo

Stochastic PDEs and Dynamics

Autor Boling Guo, Xueke Pu, Hongjun Gao
en Limba Engleză Hardback – 21 noi 2016
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 It formula
OU processes and SDEs
Random attractors
Applications
Bibliography
Index
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Specificații

ISBN-13: 9783110495102
ISBN-10: 3110495104
Pagini: 228
Ilustrații: 30 Schwarz-Weiß- Abbildungen, 10 Schwarz-Weiß- Tabellen
Dimensiuni: 175 x 246 x 18 mm
Greutate: 0.57 kg
Editura: De Gruyter

Notă biografică

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

Cuprins

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