On estimation of expectation of simultaneous renewal time of time-inhomogeneous Markov chains using dominating sequence
Volume 6, Issue 3 (2019), pp. 333–343
Pub. online: 14 October 2019
Type: Research Article
Open Access
Open Access
Received
16 March 2019
16 March 2019
Revised
14 August 2019
14 August 2019
Accepted
14 August 2019
14 August 2019
Published
14 October 2019
14 October 2019
Abstract
The main subject of the study in this paper is the simultaneous renewal time for two time-inhomogeneous Markov chains which start with arbitrary initial distributions. By a simultaneous renewal we mean the first time of joint hitting the specific set C by both processes. Under the condition of existence a dominating sequence for both renewal sequences generated by the chains and non-lattice condition for renewal probabilities an upper bound for the expectation of the simultaneous renewal time is obtained.
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