Stability of Infinite Dimensional Stochastic Differential Equations with Applications
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A01=Kai Liu
Asymptotic Stability
Author_Kai Liu
Banach Space
Bounded Linear Operators
Category=PBKJ
Category=PBT
Category=PBW
Category=PHU
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evolution
exponential
Exponentially Stable
feedback stabilization
functional differential equations
Global Strong Solution
hilbert
Hilbert space analysis
infinite dimensional stochastic systems stability
Invariant Measure
Lipschitz Continuous Function
Lyapunov Functions
Markov Process Xt
mild
Mild Solutions
navier
Navier-Stokes modeling
Nonlinear Stochastic Systems
Nonnegative Continuous Function
Null Solution
reaction-diffusion systems
real
Real Separable Hilbert Space
separable
Separable Banach Space
solution
Solution Xt
space
stochastic control theory
Stochastic Equations
Stochastic Evolution Equations
Stochastic Integrals
Stochastic Navier Stokes Equations
Stochastic Parabolic Equations
Strong Solution
Totally Bounded
Ultimately Bounded
Unique Mild Solution
Product details
- ISBN 9780367392253
- Weight: 430g
- Dimensions: 156 x 234mm
- Publication Date: 05 Sep 2019
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Paperback
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Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well established, the study of their stability properties has grown rapidly only in the past 20 years, and most results have remained scattered in journals and conference proceedings.
This book offers a systematic presentation of the modern theory of the stability of stochastic differential equations in infinite dimensional spaces - particularly Hilbert spaces. The treatment includes a review of basic concepts and investigation of the stability theory of linear and nonlinear stochastic differential equations and stochastic functional differential equations in infinite dimensions. The final chapter explores topics and applications such as stochastic optimal control and feedback stabilization, stochastic reaction-diffusion, Navier-Stokes equations, and stochastic population dynamics.
In recent years, this area of study has become the focus of increasing attention, and the relevant literature has expanded greatly. Stability of Infinite Dimensional Stochastic Differential Equations with Applications makes up-to-date material in this important field accessible even to newcomers and lays the foundation for future advances.
Liu, Kai
