IFRA Properties of Some Markov Jump Processes with General State Space

Consider a stochastically monotone increasing regular Markov jump process on a partially ordered measurable space 𝒳. It is shown that the first passage time to any upper set U is IFRA. A conjecture of Brown and Chaganty (Brown, M., Chaganty, N. R. 1983. On the first passage time distribution for a class of Markov chains. Ann. Probab.11 1000–1008.) is verified and results of Brown and Chaganty (Brown, M., Chaganty, N. R. 1983. On the first passage time distribution for a class of Markov chains. Ann. Probab.11 1000–1008.) and of Ross (Ross, S. M. 1981. Generalized Poisson shock models. Ann. Probab.9 896–898.) are extended.