Random time-changes and asymptotic results for a class of continuous-time markov chains on integers with alternating rates

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. This kind of processes are useful in the study of chain molecular diffusions. We give explicit formulas for probability generating functions, and also for means, variances and state probabilities of the random variables of the process. More-over we study independent random time-changes with the inverse of the stable subordinator, the stable subordinator and the tempered stable subordinator. We also present some asymptotic results in the fashion of large deviations. These results give some generalizations of those presented in [Journal of Statistical Physics 154 (2014), 1352–1364].