Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31515
A Study on Stochastic Integral Associated with Catastrophes

Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan


We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).

Keywords: Stochastic integrals, single–server queue model, catastrophes, busy period.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 545


[1] Anderson, W. J. (1991). “Continuous-Time Markov Chains: An Applications-Oriented Approach”. Springer, New York.
[2] Brockwell, P. J. (1985). “The extinction time of a birth, death and catastrophe process and of a related diffusion model”. Adv. Appl. Prob. 17, 42-52.
[3] Brockwell, P. J., Gani, J. And Resnick, S. I. (1982). “Birth, immigration and catastrophe processes”. Adv. Appl. Prob. 14, 709-731.
[4] Chen, A., Pollett, P. K., Zhang, H. And Cairns, B. (2003).”Uniqueness Criteria for continuous-time Markov chains with general transition structure”. Submitted. Available.
[5] Ezhov, I. I. And Reshetnyak, V. N. (1983). “Amodification of the branching process”.Ukranian Math. J. 35, 28-33.
[6] Harris, T. E. (1963). “The Theory of Branching Processes”. Springer, Berlin.intermaths.
[7] Krishna Kumar, B.; Arivudainambi, D. “Transient solution of an M/M/1 queue with catastrophes. Comput. Math. Appl. 2000, 40, 1233–1240.
[8] Mangel, M. And Tier, C. (1993). “Dynamics of meta populations with demographic stochasticity and environmental catastrophes”. Theoret. Pop. Biol. 44, 1-31.
[9] Pakes, A. G. (1987). “Limit theorems for the population size of a birth and death process allowing catastrophes”. J. Math. Biol. 25, 307-325.
[10] Pakes, A. G. (1989). “Asymptotic results for the extinction time of Markov branching processes allowing emigration”. I. Random walk decrements. Adv. Appl. Prob. 21, 243-269.