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Time-dependent rate conservation laws for a process defined with a stationary marked point process and their applications

Part of: Markov processes Stochastic processes Special processes

Published online by Cambridge University Press:  14 July 2016

Masakiyo Miyazawa
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
*
∗ Postal address: Department of Information Science, Science University of Tokyo, Noda, Chiba 278, Japan.
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Abstract

We derive two kinds of rate conservation laws for describing the time-dependent behavior of a process defined with a stationary marked point process and starting at time 0. These formulas are called TRCLs (time-dependent rate conservation laws). It is shown that TRCLs are useful to study the transient behaviors of risk and storage processes with stationary claim and supply processes and with a general premium and release rates, respectively. Detailed discussions are given for the severity for the risk process, and for the workload process of a single-server queue.

Keywords

TRANSIENT BEHAVIORRISK PROCESSRUIN TIMESEVERITYSTORAGE PROCESSWORKLOAD PROCESSSINGLE-SERVER QUEUEPALM DISTRIBUTION

MSC classification

Primary: 60G55: Point processes
Secondary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 60K25: Queueing theory 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 1 , March 1994 , pp. 114 - 129
Copyright
Copyright © Applied Probability Trust 1994 

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