Stochastic Evolution Systems Linear Theory and Applications to Non-L
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 stoc
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Boris L. Rozovsky · Sergey V. Lototsky
Stochastic Evolution Systems Linear Theory and Applications to Non-Linear Filtering Second Edition
Probability Theory and Stochastic Modelling Volume 89
Editors-in-chief Peter W. Glynn, Stanford, CA, USA Andreas E. Kyprianou, Bath, UK Yves Le Jan, Orsay, France Advisory Board Søren Asmussen, Aarhus, Denmark Martin Hairer, Coventry, UK Peter Jagers, Gothenburg, Sweden Ioannis Karatzas, New York, NY, USA Frank P. Kelly, Cambridge, UK Bernt Øksendal, Oslo, Norway George Papanicolaou, Stanford, CA, USA Etienne Pardoux, Marseille, France Edwin Perkins, Vancouver, Canada Halil Mete Soner, Zürich, Switzerland
The Probability Theory and Stochastic Modelling series is a merger and continuation of Springer’s two well established series Stochastic Modelling and Applied Probability and Probability and Its Applications series. It publishes research monographs that make a significant contribution to probability theory or an applications domain in which advanced probability methods are fundamental. Books in this series are expected to follow rigorous mathematical standards, while also displaying the expository quality necessary to make them useful and accessible to advanced students as well as researchers. The series covers all aspects of modern probability theory including • • • • • •
Gaussian processes Markov processes Random fields, point processes and random sets Random matrices Statistical mechanics and random media Stochastic analysis
as well as applications that include (but are not restricted to): • Branching processes and other models of population growth • Communications and processing networks • Computational methods in probability and stochastic processes, including simulation • Genetics and other stochastic models in biology and the life sciences • Information theory, signal processing, and image synthesis • Mathematical economics and finance • Statistical methods (e.g. empirical processes, MCMC) • Statistics for stochastic processes • Stochastic control • Stochastic models in operations research and stochastic optimization • Stochastic models in the physical sciences
More information about this series at http://www.springer.com/series/13205
Boris L. Rozovsky • Sergey V. Lototsky
Stochastic Evolution Systems Linear Theory and Applications to Non-Linear Filtering Second Edition
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Boris L. Rozovsky Division of Applied Mathematics Brown University Providence Rhode Island, USA
Sergey V. Lototsky Department of Mathematics University of Southern California Los Angeles California, USA
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. Original Russian language edition: ЭВОЛЮЦИОННЫЕ СТОХАСТИЧЕСКИЕ СИСТЕМЫ, published by Nauka Publishers, Moscow, 1983 ISSN 2199-3130 ISSN 2199-3149 (electronic) Probability Theory and Stochastic Modelling ISBN 978-3-319-94892-8 ISBN 978-3-319-94893-5 (eBook) https://doi.org/10.1007/978-3-319-94893-5 Libra
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