Fundamentals of Stochastic Filtering

• Main Authors: Bain, Alan. (Author), Crisan, Dan. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2009.
• Series: Stochastic Modelling and Applied Probability, 60
• Subjects: Mathematics.; Finance.; Numerical analysis.; Distribution (Probability theory).; Probability Theory and Stochastic Processes.; Control, Robotics, Mechatronics.; Numerical Analysis.; Quantitative Finance.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-76896-0

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:

• Introduction
• The Stochastic Process
• The Filtering Equations
• Uniqueness of the Solution to the Zakai and the Kushner-Stratonovitch Equations
• Other results
• Finite Dimensional Filters
• The Density of the Conditional Distribution of the Signal
• Numerical Methods for Solving the Filtering Problem
• A Continuous Time Particle Filter
• Particle Filters in Discrete Time
• Measure Theory
• Stochastic Analysis
• References.