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EXACT DISTRIBUTION OF INTERMITTENTLY CHANGING POSITIVE AND NEGATIVE COMPOUND POISSON PROCESS DRIVEN BY AN ALTERNATING RENEWAL PROCESS AND RELATED FUNCTIONS

Published online by Cambridge University Press:  30 March 2015

Yifan Xu ,
Shyamal K. De  and
Shelemyahu Zacks
Yifan Xu
Affiliation:
Department of Epidemiology and Biostatistics, Case Western Reserve University, Cleveland, OH 44106, USA E-mail: [email protected]
Shyamal K. De
Affiliation:
School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar 751005, Odisha, India E-mail: [email protected]
Shelemyahu Zacks
Affiliation:
Department of Mathematical Sciences, Binghamton University Binghamton, NY 13902, USA E-mail: [email protected]
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Abstract

Alternating renewal processes have been widely used to model social and scientific phenomenal where independent “on” and “off” states alternate. In this paper, we study a model where the value of a process cumulates and declines according to two modes of compound Poisson processes with respect to an underlying alternating renewal process. The model discussed in the present paper can be used as a revenue management model applied to inventory or to finance. The exact distribution of the process is derived as well as the double Laplace transform with respect to the level and time of the process.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 3 , July 2015 , pp. 385 - 397
Copyright
Copyright © Cambridge University Press 2015 

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