Behavior of an Almost Semicontinuous Poisson Process on a Markov Chain   Upon Attainment of A Level
  We consider the almost semi-continuous processes defined on a finite Markov chain. The representation of the moment generating functions for the absolute maximum after achievement positive level and for the recovery time are obtained. Modified processes with two-step rate of negative jumps are investigated. 
Ievgen Karnaukh
math.PR