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A process by chain dependent growth rate. part II: The ruin and ergodic problems

Published online by Cambridge University Press:  01 July 2016

Julian Keilson  and
S. Subba Rao
Julian Keilson
Affiliation:
University of Rochester, Rochester, New York
S. Subba Rao
Affiliation:
Case Western Reserve University, Cleveland
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Extract

In the homogeneous process X(t) defined on a finite irreducible Markov chain R(t) was studied. The process was characterized by an overall transition rate v per unit time, a matrix β of transition probabilities for the chain and a linear growth for X(t) dependent on the chain; viz. dX(t)/dt|R(t) = i = vi. The central limit behavior of the process was exhibited in. For the case when the chain had only two states, the ruin and ergodic problems were considered in for the bounded process. The object of this paper is to investigate the ruin and ergodic problems for the process of in the presence of boundaries.

Type
Research Article
Information
Advances in Applied Probability , Volume 3 , Issue 2 , Autumn 1971 , pp. 315 - 338
Copyright
Copyright © Applied Probability Trust 1971 

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References

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