IFRA Properties of Some Markov Jump Processes with General State Space

1 August 1987

journal article
Published by Institute for Operations Research and the Management Sciences (INFORMS) in Mathematics of Operations Research

Vol. 12 (3) , 562-568
https://doi.org/10.1287/moor.12.3.562

Abstract

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.

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