an:01537440
Zbl 0958.60076
Gusak, D. V.
On a generalized semicontinuous integer-valued Poisson process with reflection
EN
Theory Probab. Math. Stat. 59, 41-46 (1999); translation from Teor. Jmorvirn. Mat. Stat. 59, 41-46 (1998).
00072053
1998
j
60J50 60J70 60K10 60K15
semi-continuous Poisson process with reflection; resolvent of process
For continuous from below Poisson process \(\xi(t)\) with integer-valued jumps relations for the generating function of extrema are established. The distribution of the modified process \(\xi_{x}(t)\) with instantaneous reflection on lower bound is expressed by these generating functions. For the process \(\xi_{x}(t)\) under conditions of ergodicity the limiting distribution is found. This distribution is determined by the distribution of the absolute maximum of the given process \(\xi(t).\) Relations for generating functions of the first exit time out of a finite interval for the process \(\xi(t)\) in terms of resolvent of the process \(\xi(t)\) are established. This resolvent is determined by the distribution of the extrema of the process \(\xi(t)\).
A.V.Swishchuk (Ky??v)