Versions of a compound Poisson process
Д. В. Гусак · Theory of Probability and Mathematical Statistics · 2005
We consider two versions of an oscillating compound Poisson process with reflections from two boundaries. The versions are constructed from an upper continuous compound Poisson process $\xi (t)$ and two functionals of it, namely the exit time from an interval and first upcrossing or downcrossing times from the upper or lower boundaries, respectively. The basic characteristics of the processes considered in the paper are given in terms of the potential and resolvent of the process $\xi (t)$ introduced earlier by V. S. Korolyuk.