Solving the Zakai equation by ito's Method

2006 ◽  
pp. 155-161
Author(s):  
V. E. Beneš
Keyword(s):  
Zakai Equation

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.

Model Problem for Integro-Differential Zakai Equation with Discontinuous Observation Processes

2011 ◽  
Vol 64 (1) ◽  
pp. 37-69 ◽  
Author(s):  
R. Mikulevicius ◽  
H. Pragarauskas
Keyword(s):  
Model Problem ◽  
Zakai Equation

Real time solution of Duncan-Mortensen-Zakai equation without memory

2008 ◽  
Author(s):  
Stephen S.-T. Yau ◽  
Shing-Tung Yau
Keyword(s):  
Real Time ◽  
Zakai Equation ◽  
Time Solution

Fractional generalizations of filtering problems and their associated fractional Zakai equations

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Sabir Umarov ◽  
Frederick Daum ◽  
Kenric Nelson
Keyword(s):  
Brownian Motion ◽  
Fractional Derivative ◽  
Lévy Process ◽  
Nonlinear Filtering ◽  
Levy Process ◽  
Zakai Equation ◽  
Filtering Problem

AbstractIn this paper we discuss fractional generalizations of the filtering problem. The ”fractional” nature comes from time-changed state or observation processes, basic ingredients of the filtering problem. The mathematical feature of the fractional filtering problem emerges as the Riemann-Liouville or Caputo-Djrbashian fractional derivative in the associated Zakai equation. We discuss fractional generalizations of the nonlinear filtering problem whose state and observation processes are driven by time-changed Brownian motion or/and Lévy process.

A Zakai equation derivation of the extended Kalman filter

Automatica ◽  
2010 ◽  
Vol 46 (3) ◽  
pp. 620-624 ◽  
Author(s):  
Robert J. Elliott ◽  
Simon Haykin
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Zakai Equation

scholarly journals Reduction of the Zakai equation by invariance group techniques

1998 ◽  
Vol 73 (1) ◽  
pp. 119-130 ◽  
Author(s):  
Michel Cohen de Lara
Keyword(s):  
Invariance Group ◽  
Zakai Equation

scholarly journals Itô's formula in UMD Banach spaces and regularity of solutions of the Zakai equation

2008 ◽  
Vol 245 (1) ◽  
pp. 30-58 ◽  
Author(s):  
Z. Brzeźniak ◽  
J.M.A.M. van Neerven ◽  
M.C. Veraar ◽  
L. Weis
Keyword(s):  
Banach Spaces ◽  
Regularity Of Solutions ◽  
Itô’S Formula ◽  
Zakai Equation ◽  
Itô's Formula ◽  
Ito’S Formula ◽  
Umd Banach Spaces ◽  
Ito's Formula

scholarly journals Time-discretization of the zakai equation for diffusion processes observed in correlated noise

1991 ◽  
Vol 35 (4) ◽  
pp. 233-256 ◽  
Author(s):  
Patrick Florchinger ◽  
FranÇois le Gland
Keyword(s):  
Diffusion Processes ◽  
Time Discretization ◽  
Correlated Noise ◽  
Zakai Equation

scholarly journals On Hölder solutions of the integro-differential Zakai equation

2009 ◽  
Vol 119 (10) ◽  
pp. 3319-3355 ◽  
Author(s):  
R. Mikulevicius ◽  
H. Pragarauskas
Keyword(s):  
Zakai Equation

On the solution of the Zakai equation for the process diagnostics problem

1984 ◽  
Author(s):  
Kenneth Loparo ◽  
Zvi Roth
Keyword(s):  
Zakai Equation ◽  
Process Diagnostics
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