We consider a telegraph process with elastic boundary at the origin studied recently in the literature. It is a particular random motion with finite velocity which starts at $xgeq 0$, and its dynamics is determined by upward and downward switching ra
tes $lambda$ and $mu$, with $lambda>mu$, and an absorption probability (at the origin) $alphain(0,1]$. Our aim is to study the asymptotic behavior of the absorption time at the origin with respect to two different scalings: $xtoinfty$ in the first case; $mutoinfty$, with $lambda=betamu$ for some $beta>1$ and $x>0$, in the second case. We prove several large and moderate deviation results. We also present numerical estimates of $beta$ based on an asymptotic Normality result for the case of the second scaling.
We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state probabilities of th
e random variables of the process. Moreover we study independent random time-changes with the inverse of the stable subordinator, the stable subordinator and the tempered stable subodinator. We also present some asymptotic results in the fashion of large deviations. These results give some generalizations of those presented in Di Crescenzo A., Macci C., Martinucci B. (2014).
