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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
€129.95
Tabella dei contenuti
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
Circa l’autore
Boling Guo, Inst. of Applied Physics & Computational Maths;Hongjun Gao, Nanjing Normal Univ.;Xueke Pu, Chongqing Univ., China.
Lingua Inglese ● Formato EPUB ● Pagine 228 ● ISBN 9783110492439 ● Dimensione 34.6 MB ● Casa editrice De Gruyter ● Città Berlin/Boston ● Pubblicato 2016 ● Edizione 1 ● Scaricabile 24 mesi ● Moneta EUR ● ID 6587196 ● Protezione dalla copia Adobe DRM
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