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- Title
Sojourn time of almost semicontinuous integral-valued processes in a fixed state.
- Authors
Gusak, D.
- Abstract
Let ξ( t) be an almost lower semicontinuous integer-valued process with moment generating function of the negative parts of jumps For the moment generating function of the sojourn time of ξ( t) in a fixed state, we deduce relations in terms of the roots $ {z_s} < 1 < {\hat{z}_s} $ of the Lundberg equation. Passing to the limit as s → 0 in the relations obtained as a result, we determine the distributions of l(∞).
- Subjects
CONTINUOUS functions; INTEGRALS; GENERATING functions; JUMP processes; ROOTS of equations; MATHEMATICAL analysis
- Publication
Ukrainian Mathematical Journal, 2012, Vol 63, Issue 8, p1176
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-012-0571-y