Explicit solution of a Kolmogorov equation
type: Item
instance of: scholarly article
title: Explicit solution of a Kolmogorov equation
zbMATH Open document ID: 0862.35017
DOI: 10.1007/BF01182625
published in: Applied Mathematics and Optimization
publication date: 1996-12-03T00:00:00Z
review text: A rather wide class of nonlinear filtering systems with arbitrary nonlinear drift, which satisfies only some regularity assumption at infinity, is considered. A new method to solve Kolmogorov equation (i.e., Duncan-Mortensen-Zakai equation with observation \(h(x)=\text{constant}\)), which is well-known to be a fundamental equation in electrical engineering, is given. This method allows one to write down the formal solution of Kolmogorov equation explicitly in a closed form. From the truncated formal solution a convergent solution is constructed and the time interval on which that solution converges is estimated.
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 938675
zbMATH Keywords: finite-dimensional filters
zbMATH Keywords: nonlinear drift
zbMATH Keywords: truncated formal solution
author: Shing-Tung Yau
author: Stephen Yau
reviewed by: Valery V. Karachik
MaRDI profile type: Publication
cites work: Exact finite-dimensional filters for certain diffusions with nonlinear drift
cites work: Q3960561
cites work: Des resultats de non existence de filtre de dimension finie
cites work: Finite-Dimensional Filters with Nonlinear Drift. II: Brockett’s Problem on Classification of Finite-Dimensional Estimation Algebras
cites work: Finite-Dimensional Filters with Nonlinear Drift IV: Classification of Finite-Dimensional Estimation Algebras of Maximal Rank with State–Space Dimension 3
cites work: Some remarks on estimation algebras
cites work: On a multiplicative functional transformation arising in nonlinear filtering theory
cites work: Q3953669
cites work: Structure and Classification Theorems of Finite-Dimensional Exact Estimation Algebras
cites work: Stochastic differential equations for the non linear filtering problem
cites work: On a Necessary and Sufficient Condition for Finite Dimensionality of Estimation Algebras
cites work: On Global Representations of the Solutions of Linear Differential Equations as a Product of Exponentials
cites work: Q4084640
cites work: New classes of finite-dimensional nonlinear filters
cites work: On a new class of finite dimensional estimation algebras
cites work: Theorems on the structure of finite dimensional estimation algebras
cites work: Q4296272
full work available at URL: https://doi.org/10.1007/bf01182625
OpenAlex ID: W2083667557
description: scientific article; zbMATH DE number 938675