On estimating exponential moment for the simultaneous renewal time for two random walks on a half line
DOI:
https://doi.org/10.17721/1812-5409.2021/2.4Keywords:
renewal theory, coupling, time-inhomogeneous Markov chainsAbstract
In this paper, we consider conditions for existence and finitness for an exponential moment for the time of the simultaneous hitting of a given set by two random walks on a half-line. It is addmitted that random walks may be time-inhomogeneous. Obtained conditions that guarantee existence of the hitting time for individual chains and simultaneous hitting time for both chains. It is shown, how the estimates could be calculated in practical applications.
Pages of the article in the issue: 26 - 31
Language of the article: Ukrainian
References
R. Douc, E. Moulines, P. Priouret and P. Soulier, (2018) “Markov Chains”, (Springer International Publishing, 2018), p. 757.
Golomoziy V. (2021) “Computable bounds of exponential moments of simultaneous hitting time for two time-inhomogeneous atomic Markov chains”, Proceedings of the International Conference on Stochastic Processes and Algebraic Structures, In Print.
Golomoziy V. (2021) “Exponential moments of simultaneous hitting time for non-atomic Markov chains”, Glasnik Matematicki, In print.
S. Meyn and R.L. Tweedie (2009) “Markov Chains and Stochastic Stability”, 2nd edn. (Cambridge University Press, 2009), p. 624.
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