On the Moment-Generating Functions of Extrema and Their Complements for Almost Semicontinuous Integer-Valued Poisson Processes on Markov Chains
AbstractFor an integer-valued compound Poisson process with geometrically distributed jumps of a certain sign [these processes are called almost upper (lower) semicontinuous] defined on a finite regular Markov chain, we establish relations (without projections) for the moment-generating functions of extrema and their complements. Unlike the relations obtained earlier in terms of projections, the proposed new relations for the moment-generating functions are determined by the inversion of the perturbed matrix cumulant function. These matrix relations are expressed via the moment-generating functions for the distributions of the corresponding jumps.
How to Cite
Herych, M. S., and D. V. Gusak. “On the Moment-Generating Functions of Extrema and Their Complements for Almost Semicontinuous Integer-Valued Poisson Processes on Markov Chains”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 8, Aug. 2015, pp. 1034-49, https://umj.imath.kiev.ua/index.php/umj/article/view/2044.