We consider a Bernoulli process where the success probability changes with respect to a Markov chain. Such a model represents an interesting application of stochastic processes where the parameters are not constants; rather, they are stochastic processes themselves due to their dependence on a...

We consider ordinary and conditional first passage times in a general birth–death process. Under existence conditions, we derive closed-form expressions for the kth order moment of the defined random variables, k ≥ 1. We also give an explicit condition for a birth–death process to be...