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Moments of Random Allocation Processes Reaching a Boundary

Part of: Physiological, cellular and medical topics Stochastic processes

Published online by Cambridge University Press:  14 July 2016

G. S. Tsitsiashvili
G. S. Tsitsiashvili*
Affiliation:
Russian Academy of Sciences
*
∗Postal address: Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Radio str. 7, 690041 Vladivostok, Russia. Email address: [email protected]
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Abstract

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In this paper we develop some results presented by Gani (2004), deriving moments for random allocation processes. These moments correspond to the allocation processes reaching some domain boundary. Exact formulae for means, variances, and probability generating functions as well as some asymptotic formulae for moments of random allocation processes are obtained. A special choice of the asymptotics and of the domain allows us to reduce a complicated numerical procedure to a simple asymptotic one.

Keywords

Infectivesusceptibleallocation processurn schemelaw of large numbersdomain boundary

MSC classification

Secondary: 60G20: Generalized stochastic processes 92C60: Medical epidemiology
Type
Research Papers
Information
Journal of Applied Probability , Volume 44 , Issue 4 , December 2007 , pp. 990 - 995
Copyright
Copyright © Applied Probability Trust 2007 

References

[1] Gani, J. (2004). Random-allocation and urn models. In Stochastic Methods and Their Applications (J. Appl. Prob. Spec. Vol. 41A), Applied Probability Trust, Sheffield, pp. 313–320.Google Scholar
[2] Tsitsiashvili, G. S. (1995). Transformation of an epidemic model to a random walk and its management. Math. Scientist 20, 103–106.Google Scholar