The Oxford handbook of nonlinear filtering /
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| Imprint: | Oxford ; New York : Oxford University Press, 2011. |
|---|---|
| Description: | xiv, 1063 p. : ill. ; 26 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8367769 |
Table of Contents:
- 1. Introduction
- 2. The Foundations of Nonlinear Filtering
- 2.1. Nonlinear Filtering Problems
- I. Bayes Formulae and Innovations
- 2.2. Nonlinear Filtering Problems
- II. Associated Equations
- 2.3. Nonlinear Filtering Equations for Processes With Jumps
- 2.4. The Filtered Martingale Problem
- 3. Nonlinear Filtering and Stochastic Partial Differential Equations
- 3.1. Filtering Equations for Partially Observable Diffusion Processes With Lipschitz Continuous Coefficients
- 3.2. Malliavin Calculus Applications to the Study of Nonlinear Filtering
- 3.3. Chaos Expansion to Nonlinear Filtering
- 4. Stability and Asymptotic Analysis
- 4.1. On Filtering with Unspecified Initial Data for Non-uniformly Ergodic Signals
- 4.2. Exponential Decay Rate of the Filter's Dependence on the Initial Distribution
- 4.3. Intrinsic Methods in Filter Stability
- 4.4. Feller and Stability Properties of the Nonlinear Filter
- 4.5. Lipschitz Continuity of Feynman-Kac Propagators
- 5. Special Topics
- 5.1. Pathwise Nonlinear Filtering
- 5.2. The Innovation Problem
- 5.3. Nonlinear Filtering and Fractional Brownian Motion
- 6. Estimation and Control
- 6.1. Dual Filters, Path Estimators and Information
- 6.2. Filtering for Discrete-Time Markov Processes and Applications to Inventory Control with Incomplete Information
- 6.3. Bayesian Filtering of Stochastic Hybrid Systems in Discrete-time and Interacting Multiple Model
- 7. Approximation Theory
- 7.1. Error Bounds for the Nonlinear Filtering of Diffusion Processes
- 7.2. Discretizing the Continuous Time Filtering Problem. Order of Convergence
- 7.3. Large Sample Asymptotics for the Ensemble Kalman Filter
- 8. The Particle Approach
- 8.1. Particle Approximations to the Filtering Problem in Continuous Time
- 8.2. Tutorial on Particle Filtering and Smoothing: Fifteen Years Later
- 8.3. A Mean Field Theory of Nonlinear Filtering
- 8.4. The Particle Filter in Practice
- 8.5. Introducing Cubature to Filtering
- 9. Numerical Methods in Nonlinear Filtering
- 9.1. Numerical Approximations to Optimal Nonlinear Filters
- 9.2. Signal Processing Problems on Function Space: Bayesian Formulation, SPDEs and Effective MCMC Methods
- 9.3. Robust, Computationally Efficient Algorithms for Tracking Problems with Measurement Process Nonlinearities
- 9.4. Nonlinear Filtering Algorithms Based on Averaging Over Characteristics and on the Innovation Approach
- 10. Nonlinear Filtering in Financial Mathematics
- 10.1. Nonlinear Filtering in Models for Interest-Rate and Credit Risk
- 10.2. An Asset Pricing Model with Mean Reversion and Regime Switching Stochastic Volatility
- 10.3. Portfolio Optimization Under Partial Observation: Theoretical and Numerical Aspects
- 10.4. Filtering with Counting Process Observations: Application to the Statistical Analysis of the Micromovement of Asset Price
