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Stochastic PDEs and Dynamics

Boling Guo, Hongjun Gao, Xueke Pu (Autoren)

Buch | Hardcover

VIII, 220 Seiten

2016
De Gruyter (Verlag)
978-3-11-049510-2 (ISBN)

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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:PreliminariesThe stochastic integral and Itô formulaOU processes and SDEsRandom attractorsApplicationsBibliographyIndex

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

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

Erscheinungsdatum	11.10.2016
Zusatzinfo	30 b/w ill., 10 b/w tbl.
Verlagsort	Berlin/Boston
Sprache	englisch
Maße	170 x 240 mm
Gewicht	560 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	dynamical behavior • Itô's formula • Ornstein-Uhlenbeck processes • random attractors • stochastic integrals • Stochastic PDEs
ISBN-10	3-11-049510-4 / 3110495104
ISBN-13	978-3-11-049510-2 / 9783110495102
Zustand	Neuware