Stochastic Filtering for Partially Observed Diffusions
Filtering Equations, Density Methods, and Particle Approximations
Contents
- Preface
- List of Figures
- List of Tables
- 1Conditional Distributions and Partial Observation
- 2Signal Models and Prediction
- 3Bayesian Updates and Discrete Observations
- 4Linear Gaussian Filtering
- 5Reference Measures and Unnormalised Filters
- 6Innovations and the Nonlinear Filtering Equation
- 7Finite-State Filters and Finite-Dimensional Closure
- 8Stability, Forgetting and Model Error
- 9Conditional Densities and Their Equations
- 10Density Approximations and Projection Filters
- 11Particle Approximations and Resampling
- 12Approximation Guarantees and Decisions under Partial Observation
- References
- Index
- About the Author
About this book
What does an observation allow us to conclude about a hidden diffusion?
The answer is a conditional distribution. This book follows that distribution from conditional expectation and Bayesian updating to the equations of nonlinear filtering, then to the approximations needed when exact closure fails.
Kalman–Bucy filtering provides an exact Gaussian benchmark. Reference measures, the Zakai equation and innovations lead to the general filtering equations. Later chapters develop stability, conditional densities, projection methods and particle approximations, keeping the target law and the assumptions of each construction explicit.
Analytic contours, worked examples, proofs and full algorithm descriptions connect the theory to concrete calculations. The final chapter separates approximation errors and examines how errors in a posterior affect a decision.
For graduate students, researchers and mathematically trained practitioners with a background in probability, Itô calculus, linear algebra and elementary differential equations.
The covers
