Fundamentals of Stochastic Filtering

• Main Authors: Bain, Alan (Author), Crisan, Dan (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2009.
• Series: Stochastic Modelling and Applied Probability, 60
• Subjects: Mathematics.; Economics, Mathematical.; Numerical analysis.; Probabilities.; Control engineering.; Robotics.; Mechatronics.; Probability Theory and Stochastic Processes.; Control, Robotics, Mechatronics.; Numerical Analysis.; Quantitative Finance.

The objective of stochastic filtering is to determine the best estimate for the state of a stochastic dynamical system from partial observations. The solution of this problem in the linear case is the well known Kalman-Bucy filter which has found widespread practical application. The purpose of this...

Table of Contents:

• Filtering Theory
• The Stochastic Process ?
• The Filtering Equations
• Uniqueness of the Solution to the Zakai and the Kushner–Stratonovich Equations
• The Robust Representation Formula
• Finite-Dimensional Filters
• The Density of the Conditional Distribution of the Signal
• Numerical Algorithms
• Numerical Methods for Solving the Filtering Problem
• A Continuous Time Particle Filter
• Particle Filters in Discrete Time.