Stochastic Evolution Systems
Linear Theory and Applications to Non-Linear Filtering
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Beschreibung
This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations.
The emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems.
This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.
This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations.
The emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems.
This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.
Provides a self-contained development of the theory of generalized solutions of stochastic parabolic equations Explores equations of optimal non-linear filtering, interpolation, and extrapolation of diffusion processes in detail Establishes various connections between diffusions and linear stochastic parabolic equations
Autor*in
Boris L. Rozovsky
Themen in »Stochastic Evolution Systems«
MSC (2010): 60H15, 35R60 Boundary value problem Markov property Martingale Sobolev space diffusion process filtering problem local martingale partial differential equation backward diffusion equation chaos solution of parabolic equations interpolation extrapolation Hormander's condition in filtering stochastic characteristics
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“The book will be useful for those who are working in the area of applications of stochastic evolution systems in physics, biology and control theory, and require tools from stochastic analysis and partial differential equations.” (Anatoliy Swishchuk, zbMATH 1434.60004, 2020)
“A remarkable quality of this monograph is that the results are stated and proved with a great level of generality and rigor. The reader will find many interesting results, as well as lots of long and technical proofs … .” (Charles-Edouard Bréhier, Mathematical Reviews, October, 2019)
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