@article{Herych_Gusak_2015, title={On the Moment-Generating Functions of Extrema and Their Complements for Almost Semicontinuous Integer-Valued Poisson Processes on Markov Chains}, volume={67}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2044}, abstractNote={For 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.}, number={8}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={HerychM. S. and GusakD. V.}, year={2015}, month={Aug.}, pages={1034-1049} }