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On termination time processes

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Jewgeni H. Dshalalow
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Abstract

In this paper we study the behavior of a delayed compound renewal process, S, about some fixed level, L. Normally, a jump process S increases at random times τ1, τ2, …, in random increments until it crosses L. S would then be terminated in a random number v of phases at time τv. In many applications, a more general termination scenario assumes that S may evolve either through v or σ random phases, whichever of the two is smaller (denoted by T). The number T of actual phases is called the termination index, and we evaluate a joint functional of T, the termination time τ T and the termination level ST. We also seek information about the process S a step before its termination, and derive a joint functional for all relevant processes. Examples of these processes and their applications to various stochastic models are discussed.

Keywords

FIRST-PASSAGE PROBLEMFLUCTUATION THEORYDELAYED RENEWAL PROCESSTERMINATION PROCESSTERMINATION INDEXTERMINATION TIMEFIRST EXCESS LEVELPRETERMINATIONQUEUEINGINVENTORY CONTROLSTOCK MARKETPOWER STATION

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 60K15: Markov renewal processes, semi-Markov processes 60K25: Queueing theory
Type
Part 6 Stochastic Processes
Information
Journal of Applied Probability , Volume 31 , Issue A , 1994 , pp. 325 - 336
Copyright
Copyright © Applied Probability Trust 1994 

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