On estimation of expectation of simultaneous renewal time of time-inhomogeneous Markov chains using dominating sequence
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2020
- DOI:
- 10.48550/arXiv.2001.02442
- arXiv:
- arXiv:2001.02442
- Bibcode:
- 2020arXiv200102442G
- Keywords:
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- Mathematics - Probability
- E-Print:
- Published at https://doi.org/10.15559/19-VMSTA138 in the Modern Stochastics: Theory and Applications (https://vmsta.org/) by VTeX (http://www.vtex.lt/)