Stochastic PDEs and Dynamics
(Sprache: Englisch)
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...
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Klappentext zu „Stochastic PDEs and Dynamics “
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
Inhaltsverzeichnis zu „Stochastic PDEs and Dynamics “
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
Autoren-Porträt von Boling Guo, Hongjun Gao, Xueke Pu
Boling Guo, Inst. of Applied Physics & Computational Maths;Hongjun Gao, Nanjing Normal Univ.;
Xueke Pu, Chongqing Univ., China.
Bibliographische Angaben
- Autoren: Boling Guo , Hongjun Gao , Xueke Pu
- 2016, VIII, 220 Seiten, 30 Schwarz-Weiss-Abbildungen, mit Abbildungen, Masse: 17,6 x 24,6 cm, Gebunden, Englisch
- Verlag: De Gruyter
- ISBN-10: 3110495104
- ISBN-13: 9783110495102
- Erscheinungsdatum: 21.11.2016
Sprache:
Englisch
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