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The stationary probability density of a class of bounded Markov processes

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Muhamad Azfar Ramli  and
Gerard Leng
Muhamad Azfar Ramli*
Affiliation:
National University of Singapore
Gerard Leng*
Affiliation:
National University of Singapore
*
∗ Postal address: Cooperative Systems Lab E1-03-06, Department of Mechanical Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore 117576.
∗ Postal address: Cooperative Systems Lab E1-03-06, Department of Mechanical Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore 117576.
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Abstract

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In this paper we generalize a bounded Markov process, described by Stoyanov and Pacheco-González for a class of transition probability functions. A recursive integral equation for the probability density of these bounded Markov processes is derived and the stationary probability density is obtained by solving an equivalent differential equation. Examples of stationary densities for different transition probability functions are given and an application for designing a robotic coverage algorithm with specific emphasis on particular regions is discussed.

Keywords

Bounded Markov processgeneral state spacestationary densityMarkov operator

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Secondary: 60J05: Discrete-time Markov processes on general state spaces
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 4 , December 2010 , pp. 986 - 993
Copyright
Copyright © Applied Probability Trust 2010 

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