Dan Crisan, Boris Rozovskii

The Oxford Handbook of Nonlinear Filtering

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Oxford Handbooks in Mathematics
• Verlag: Oxford University Press
• Seitenzahl: 1088
• Erscheinungstermin: Februar 2011
• Englisch
• Abmessung: 253mm x 182mm x 68mm
• Gewicht: 1974g
• ISBN-13: 9780199532902
• ISBN-10: 0199532907
• Artikelnr.: 32688828

Autorenporträt

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.

Inhaltsangabe

* 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 and R. Mikulevicius: Nonlinear Filtering
Equations for Processes With Jumps
* 2.4: T. G. Kurtz and 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 and 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 and 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 and S. P. Sethi: Filtering for
Discrete-Time Markov Processes and Applications to Inventory Control
with Incomplete Information
* 6.3: H. A.P. Blom and 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 and 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 and A. M. Johansen: Tutorial on Particle Filtering and
Smoothing: Fifteen Years Later
* 8.3: P. Del Moral, F. Patras and S. Rubenthaler: A Mean Field Theory
of Nonlinear Filtering
* 8.4: T. B. Schon, F. Gustafsson and R. Karlsson: The Particle Filter
in Practice
* 8.5: C. Litterer and 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 and J. Voss: Signal Processing Problems on
Function Space: Bayesian Formulation, SPDEs and Effective MCMC
Methods
* 9.3: J. M. C. Clark and R. B. Vinter: Robust, Computationally
Efficient Algorithms for Tracking Problems with Measurement Process
Nonlinearities
* 9.4: G.N. Milstein and 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 and W. Runggaldier: Nonlinear Filtering in Models for
Interest-Rate and Credit Risk
* 10.2: R. J. Elliott, H. Miao and 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 and Y. Zeng: Filtering with Counting Process
Observations: Application to the Statistical Analysis of the
Micromovement of Asset Price