The General Filtering Problem and the Stochastic Equation of the Optimal Filter (Part I)

1980 ◽  
pp. 192-224
Author(s):  
Gopinath Kallianpur
Keyword(s):  
Stochastic Equation ◽  
Optimal Filter ◽  
Filtering Problem

scholarly journals Unbiased estimation of the solution to Zakai’s equation

2020 ◽  
Vol 26 (2) ◽  
pp. 113-129
Author(s):  
Hamza M. Ruzayqat ◽  
Ajay Jasra
Keyword(s):  
Continuous Time ◽  
Unbiased Estimation ◽  
Finite Variance ◽  
Linear Filtering ◽  
Multilevel Monte Carlo ◽  
Zakai Equation ◽  
Unbiased Estimators ◽  
First Order ◽  
Multilevel Monte Carlo Method ◽  
Filtering Problem

AbstractIn the following article, we consider the non-linear filtering problem in continuous time and in particular the solution to Zakai’s equation or the normalizing constant. We develop a methodology to produce finite variance, almost surely unbiased estimators of the solution to Zakai’s equation. That is, given access to only a first-order discretization of solution to the Zakai equation, we present a method which can remove this discretization bias. The approach, under assumptions, is proved to have finite variance and is numerically compared to using a particular multilevel Monte Carlo method.

Explicit solution to the unstable stationary filtering problem

1986 ◽  
Vol 31 (2) ◽  
pp. 185-189 ◽  
Author(s):  
U. Shaked ◽  
E. Soroka
Keyword(s):  
Explicit Solution ◽  
Filtering Problem
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