Informatics and Applications
2025, Volume 19, Issue 1, pp 25-32
FILTERING OF STATES AND PARAMETERS OF SPECIAL MARKOV JUMP PROCESSES VIA INDIRECT PERFECT OBSERVATIONS
Abstract
The paper investigates the problem of optimal state filtering of a class of stochastic differential observation systems. The state to be estimated consists of two compound components. The first is a finite-state Markov jump process. The second component changes synchronously with the first one and, given a fixed first component, forms a sequence of independent vectors. The available statistical information includes the known functions of the estimated state observed without noise. The problem is to construct the conditional distribution of the system's state given the available observations. In observation systems with degenerate noise, it is impossible to apply standard filtering techniques, which typically involve reducing the observations to a combination of Wiener and Poisson processes using a suitable Girsanov measure transform. The conditional distribution ofthe state can be represented using a recursively linked sequence ofordinary differential and difference equations.
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[+] About this article
Title
FILTERING OF STATES AND PARAMETERS OF SPECIAL MARKOV JUMP PROCESSES VIA INDIRECT PERFECT OBSERVATIONS
Journal
Informatics and Applications
2025, Volume 19, Issue 1, pp 25-32
Cover Date
2025-04-01
DOI
10.14357/19922264250104
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Markov jump process; stochastic differential observation system; indirect perfect observations;
martingale decomposition; regular version of conditional distribution
Authors
A. V. Borisov 
Author Affiliations
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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