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.

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/)

References in corpus (5)

• Renewal theory and computable convergence rates for geometrically ergodic Markov chains
• Quantitative bounds on convergence of time-inhomogeneous Markov chains
• Subgeometric ergodicity of strong Markov processes
• Practical drift conditions for subgeometric rates of convergence
• An estimate for an expectation of the simultaneous renewal for time-inhomogeneous Markov chains