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

  • Yifan Xu (a1), Shyamal K. De (a2) and Shelemyahu Zacks (a3)

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.

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1. Boxma, O., Perry, D. & Zacks, S. (2014). A fluid EOQ model of perishable items with intermittent high and low demand rates. Mathematics of Operations Research.
2. Cohen, J.W. (1982). The single server queue. Amsterdam: Elsevier Science Publishers.
3. Di Crescenzo, A., Iuliano, A., Martinucci, B. & Zacks, S. (2013). Generalized telegraph process with random jumps . Journal of Applied Probability 50: 450463.
4. Di Crescenzo, A., Martinucci, B. & Zacks, S. (2014). On the geometric Brownian motion with alternating trends. In Mathematical and Statistical Methods for Actuarial Sciences and Finance Perma, A. and Sibillo, M., , M., Eds. New York: Springer.
5. Di Crescenzo, A. & Zacks, S. (2013). Probability law and flow function of Brownian motion driven by a generalized telegraph process. Methodology and Computing in Applied Probability 120.
6. Zacks, S. (2004). Generalized integrated telegrapher process and the distribution of related stopping times. Journal of Applied Probability 41: 497507.
7. Zacks, S. (2012). Distribution of the total time in a mode of an alternating renewal process with applications. Sequential Analysis 31: 397408.

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