Stochastic Evolution Systems

Linear Theory and Applications to Non-Linear Filtering
 
 
Springer (Verlag)
  • 2. Auflage
  • |
  • erschienen am 20. Dezember 2018
 
  • Buch
  • |
  • Softcover
  • |
  • 348 Seiten
978-3-030-06933-9 (ISBN)
 
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.
Paperback
Softcover reprint of the original 2nd ed. 2018
  • Englisch
  • Cham
  • |
  • Schweiz
Springer International Publishing
  • Für Beruf und Forschung
  • Überarbeitete Ausgabe
  • 2 s/w Abbildungen
  • |
  • 2 Illustrations, black and white; XVI, 330 p. 2 illus.
  • Höhe: 235 mm
  • |
  • Breite: 155 mm
  • |
  • Dicke: 18 mm
  • 528 gr
978-3-030-06933-9 (9783030069339)
10.1007/978-3-319-94893-5
weitere Ausgaben werden ermittelt

Boris Rozovsky earned a Master's degree in Probability and Statistics, followed by a PhD in Physical and Mathematical Sciences, both from the Moscow State (Lomonosov) University. He was Professor of Mathematics and Director of the Center for Applied Mathematical Sciences at the University of Southern California. Currently, he is the Ford Foundation Professor of Applied Mathematics at Brown University.

Sergey Lototsky earned a Master's degree in Physics in 1992 from the Moscow Institute of Physics and Technology, followed by a PhD in Applied Mathematics in 1996 from the University of Southern California. After a year-long post-doc at the Institute for Mathematics and its Applications and a three-year term as a Moore Instructor at MIT, he returned to the department of Mathematics at USC as a faculty member in 2000. He specializes in stochastic analysis, with emphasis on stochastic differential equation. He supervised more than 10 PhD students and had visiting positions at the Mittag-Leffler Institute in Sweden and at several universities in Israel and Italy.

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.
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.
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