The Oxford Handbook of Nonlinear Filtering

In many areas of human endeavour, the systems involved are not available for direct measurement. Instead, by combining mathematical models for a system's evolution with partial observations of its evolving state, we can make reasonable inferences about it. The increasing complexity of the modern world makes this analysis and synthesis of high-volume data an essential feature in many real-world problems. The celebrated Kalman-Bucy filter, designed for linear dynamical systems with linearly structured measurements, is the most famous Bayesian filter. Its generalizations to nonlinear systems and/or observations are collectively referred to as nonlinear filtering (NLF), an extension of the Bayesian framework to the estimation, prediction, and interpolation of nonlinear stochastic dynamics. NLF uses a stochastic model to make inferences about an evolving system and is a theoretically optimal algorithm. The breadth of its applications, firmly established and still emerging, is simply astounding. Early uses such as cryptography, tracking, and guidance were mostly of a military nature. Since then, the scope has exploded. It includes the study of global climate, estimating the state of the economy, identifying tumours using non-invasive methods, and much more. The Oxford Handbook of Nonlinear Filtering is the first comprehensive written resource for the subject. It contains classical and recent results and applications, with contributions from 58 authors. Collated into 10 parts, it covers the foundations of nonlinear filtering, connections to stochastic partial differential equations, stability and asymptotic analysis, estimation and control, approximation theory and numerical methods for solving the nonlinear filtering problem (including particle methods). It also contains a part dedicated to the application of nonlinear filtering to several problems in mathematical finance. Contributors to this volume - R. Atar - Department of Electrical Engineering, Technion, Haifa, Israel A. Bensoussan - University of Texas at Dallas, USA H. A. P. Blom - National Aerospace Laboratory NLR, The Netherlands A. Budhiraja - University of North Carolina, USA M. Cakanyldirim - University of Texas at Dallas, USA P. Y. Chigansky - The Weizmann Institute of Science J. M. C. Clark - Imperial College London, UK D. Crisan - Imperial College London, UK M. Davis - Imperial College London, UK A. Doucet - The Institute of Statistical Mathematics, Tokyo, Japan. T. Duncan - University of Kansas, USA R. J. Elliott - University of Calgary, Australia R. Frey - Universitat Leipzig, Leipzig F. Le Gland - IRISA/INRIA, France B. Grigelionis - Lithuania F. Gustaffson - Linkoping University, Sweden M. Hairer - University of Warwick, UK R. Van Handel - Princeton University, USA A. J. Heunis - University of Waterloo, Canada A. M. Johansen - University of Warwick, UK R. Karlsson - Linkoping University, Sweden M. L. Kleptsyna - Universite du Maine, France N. V. Krylov - University of Minnesota, USA H. Kunita - Fukuoka, Japan T. Kurtz - University of Wisconsin- Madison, USA H. Kushner - Brown University, USA R. Lipster - Tel Aviv University, Israel C. Litterer - Mathematical Institute, Oxford, UK T. Lyons - Mathematical Institute, Oxford, UK S. V. Lototsky - University of Southern California, USA M. Chaleyat-Maurel - Universite Paris Descartes 45, Paris Hong Miao - Colorado State University, USA R. Mikulevicius - USC Department of Mathematics, Los Angeles, USA G. Milstein - Ural State University, Russia V. Monbet - Universite de Bretagne-Sud, France P. del Moral - Universite Bordeaux 1, France G. Nappo - University "La Sapienza ", Italy N. J. Newton - University of Essex, UK F. Patras - Universite de Nice, France H. Pham - Universites Paris 6- Paris 7, France B. Rozovski? - Brown University, USA S. Rubenthaler - Universite de Nice, France W. J. Runggaldier - Universita degli Studi di Padova, Italy T.B. Schon - Linkoping University, Sweden L. C. Scott - University of Missouri at Kansas City, USA S. P. Sethi - University of Texas at Dallas, USA Y. Bar-Shalom - University of Connecticut, USA W. Stannat - Fachbereich Mathematik A. Stuart - University of Warwick, UK V.-D. Tran - Universite de Bretagne-Sud, France M. Tretyakov - University of Leicester, UK A. Y. Veretennikov - University of Leeds, UK R. Vinter - Imperial College London, UK J. Voss - University of Warwick, UK Zhenyu Wu - University of Saskatchewan, Canada J. Xiong - Mathematics Department, Knoxville, USA O. Zeitouni - University of Minnesota, USA Y. Zeng - University of Missouri at Kansas City, USA

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