Book
Springer Proceedings in Mathematics & Statistics (Stochastic Processes, Statistical Methods, and Engineering Mathematics)
Volume 408
(2022),
p. 97
Exponential moments of simultaneous hitting time for non-atomic Markov chains
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.