Informatics and Applications
2024, Volume 18, Issue 3, pp 30-37
PROBABILISTIC ANALYSIS OF A CLASS OF MARKOV JUMP PROCESSES
- A. V. Borisov
- Yu. N. Kurinov
- R. L. Smeliansky
Abstract
The paper introduces a class of the jump processes. The first compound component represents aMarkov
jump process with a finite state space. The second compound component jumps synchronously with the first one.
Given the first component trajectory, the second component forms a sequence of independent random vectors.
The corresponding conditional distributions are known and have intersecting support sets. This makes impossible
the exact recovery of the first process component by the second one. The authors prove the Markov property for
the considered class of random processes and obtain a collection of their probability characteristics. It includes
the infinitesimal generator and its conjugate operator. Their knowledge makes possible the construction of the
Kolmogorov equation system describing the evolution of the process probability distribution. Also, a martingale
decomposition for an arbitrary function of the considered process was derived. It can be characterized by the
solution to a system of linear stochastic differential equations with martingales on the right side. If the functions of
the investigated process have finite moments of the second order, one may obtain the quadratic characteristics of
martingales.
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[+] About this article
Title
PROBABILISTIC ANALYSIS OF A CLASS OF MARKOV JUMP PROCESSES
Journal
Informatics and Applications
2024, Volume 18, Issue 3, pp 30-37
Cover Date
2024-09-20
DOI
10.14357/19922264240304
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Markov jump process; infinitisemal generator; martingale decomposition; stochastic differential equation
Authors
A. V. Borisov  ,  , Yu. N. Kurinov , and R. L. Smeliansky
Author Affiliations
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
M. V. Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1,Moscow 119991, Russian Federation
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