Stochastic evolution systems : linear theory and applications to non-linear filtering
著者
書誌事項
Stochastic evolution systems : linear theory and applications to non-linear filtering
（Probability theory and stochastic modelling, v. 89）
Springer, c2018
2nd ed
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Эволюционные стохастические системы
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注記
"1st edition (1990) translated from the Russian by A. Yarkho and published under Rozovskii, B.L. as volume 35 in the series "Mathematics and Its Applications" by Kluwer Academic Publishers"--T.p. verso
Includes bibliographical references (p. 321-327) and index
内容説明・目次
内容説明
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.
目次
1 Examples and Auxiliary Results.- 2 Stochastic Integration in a Hilbert Space.- 3 Linear Stochastic Evolution Systems in Hilbert Spaces.- 4 Ito's Second Order Parabolic Equations.- 5 Ito's Partial Differential Equations and Diffusion Processes.- 6 Filtering, Interpolation and Extrapolation of Diffusion Processes.- 7 Hypoellipticity of Ito's Second Order Parabolic Equations.- 8 Chaos Expansion for Linear Stochastic Evolution Systems.- Notes.- References.- Index.
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