Compound Poisson Processes with Two-Sided Reflection
We consider a compound oscillating Poisson process with two-sided reflection. This process is defined by an upper-semicontinuous compound Poisson process ξ(t) and its functionals, namely the first-exit time of ξ(t) from an interval and the first-exit time of ξ(t) across the upper and lower levels. W...
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| Date: | 2002 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2002
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4200 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We consider a compound oscillating Poisson process with two-sided reflection. This process is defined by an upper-semicontinuous compound Poisson process ξ(t) and its functionals, namely the first-exit time of ξ(t) from an interval and the first-exit time of ξ(t) across the upper and lower levels. We study the main characteristics of this oscillating process in terms of the potential and resolvent of the process ξ(t) introduced by Korolyuk. For this purpose, we refine the Pecherskii identities and some other results for upper-semicontinuous Poisson processes. |
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