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The Oxford Handbook of Nonlinear Filtering

The Oxford Handbook of Nonlinear Filtering

  • Author:
  • Publisher: Oxford University Press
  • ISBN: 9780199532902
  • Published In: February 2011
  • Format: Hardback , 1080 pages
  • Jurisdiction: U.K. ? Disclaimer:
    Countri(es) stated herein are used as reference only

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  • Description 
  • Contents 
  • Author 
  • Details

    • Comprehensive, providing a unique reference source for all areas of nonlinear (or stochastic) filtering
    • Up-to-date, giving a modern interpretation of the classical theory, with many recent results
    • Covers theory and practice, including modern applications of nonlinear filtering, or hidden Markov models (HMM)
    • Authoritative, with expert editors and 58 contributors who are leaders in the field

    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.

    Readership: Aimed mainly at graduate level and above, the Handbook will appeal to both pure and applied mathematicians, statisticians, economists, engineers and other scientists for whom filtering theory is important.

  • 1: D. Crisan, B. Rozovsky: Introduction
    2: The Foundations of Nonlinear Filtering
    2.1: H. Kunita: Nonlinear Filtering Problems I. Bayes Formulae and Innovations
    2.2: H. Kunita: Nonlinear Filtering Problems II. Associated Equations
    2.3: B. Grigelionis & R. Mikulevicius: Nonlinear Filtering Equations for Processes With Jumps
    2.4: T. G. Kurtz & G. Nappo: The Filtered Martingale Problem
    3: Nonlinear Filtering and Stochastic Partial Differential Equations
    3.1: N. V. Krylov: Filtering Equations for Partially Observable Diffusion Processes With Lipschitz Continuous Coefficients
    3.2: M. Chaleyat-Maurel: Malliavin Calculus Applications to the Study of Nonlinear Filtering
    3.3: S. V. Lototsky: Chaos Expansion to Nonlinear Filtering
    4: Stability and Asymptotic Analysis
    4.1: M. L. Kleptsyna & A. Y. Veretennikov: On Filtering with Unspecified Initial Data for Non-uniformly Ergodic Signals
    4.2: R. Atar: Exponential Decay Rate of the Filter's Dependence on the Initial Distribution
    4.3: P. Chigansky, R. Liptser & R. Van Handel: Intrinsic Methods in Filter Stability
    4.4: A. Budhiraja: Feller and Stability Properties of the Nonlinear Filter
    4.5: W. Stannat: Lipschitz Continuity of Feynman-Kac Propagators
    5: Special Topics
    5.1: M. Davis: Pathwise Nonlinear Filtering
    5.2: A. J. Heunis: The Innovation Problem
    5.3: T. Duncan: Nonlinear Filtering and Fractional Brownian Motion
    6: Estimation and Control
    6.1: N. J. Newton: Dual Filters, Path Estimators and Information
    6.2: A. Bensoussan, M. Cakanyildirim & S. P. Sethi: Filtering for Discrete-Time Markov Processes and Applications to Inventory Control with Incomplete Information
    6.3: H. A.P. Blom & Y. Bar-Shalom: Bayesian Filtering of Stochastic Hybrid Systems in Discrete-time and Interacting Multiple Model
    7: Approximation Theory
    7.1: O. Zeitouni: Error Bounds for the Nonlinear Filtering of Diffusion Processes
    7.2: D. Crisan: Discretizing the Continuous Time Filtering Problem. Order of Convergence
    7.3: F. Le Gland, V. Monbet & V.-D. Tran: Large Sample Asymptotics for the Ensemble Kalman Filter
    8: The Particle Approach
    8.1: J. Xiong: Particle Approximations to the Filtering Problem in Continuous Time
    8.2: A. Doucet & A. M. Johansen: Tutorial on Particle Filtering and Smoothing: Fifteen Years Later
    8.3: P. Del Moral, F. Patras & S. Rubenthaler: A Mean Field Theory of Nonlinear Filtering
    8.4: T. B. Schon, F. Gustafsson & R. Karlsson: The Particle Filter in Practice
    8.5: C. Litterer & T. Lyons: Introducing Cubature to Filtering
    9: Numerical Methods in Nonlinear Filtering
    9.1: H. J. Kushner: Numerical Approximations to Optimal Nonlinear Filters
    9.2: M. Hairer, A. Stuart & J. Voss: Signal Processing Problems on Function Space: Bayesian Formulation, SPDEs and Effective MCMC Methods
    9.3: J. M. C. Clark & R. B. Vinter: Robust, Computationally Efficient Algorithms for Tracking Problems with Measurement Process Nonlinearities
    9.4: G.N. Milstein & M. Tretyakov: Nonlinear Filtering Algorithms Based on Averaging Over Characteristics and on the Innovation Approach
    10: Nonlinear Filtering in Financial Mathematics
    10.1: R. Frey & W. Runggaldier: Nonlinear Filtering in Models for Interest-Rate and Credit Risk
    10.2: R. J. Elliott, H. Miao & Z. Wu: An Asset Pricing Model with Mean Reversion and Regime Switching Stochastic Volatility
    10.3: H. Pham: Portfolio Optimization Under Partial Observation: Theoretical and Numerical Aspects
    10.4: L. C. Scott & Y. Zeng: Filtering with Counting Process Observations: Application to the Statistical Analysis of the Micromovement of Asset Price

  • Edited by Dan Crisan, Imperial College London, UK, and Boris Rozovskii, Brown University, USA

    Dan Crisan is Reader in Mathematics at Imperial College London. His main research interest is stochastic filtering theory.

    Boris Rozovskii is Ford Foundation Professor at Brown University. His main interests are in stochastic partial differential equations (SPDEs) and their applications.

    Contributors: 
    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 - Linköping 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 - Université 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 - Université de Nice, France 
    H. Pham - Universites Paris 6- Paris 7, France
    B. Rozovski? - Brown University, USA
    S. Rubenthaler - Université 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 - Université 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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