A process by chain dependent growth rate. part II: The ruin and ergodic problems
- 1 January 1971
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 3 (2) , 315-338
- https://doi.org/10.2307/1426174
Abstract
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.Keywords
This publication has 3 references indexed in Scilit:
- A process with chain dependent growth rateJournal of Applied Probability, 1970
- A review of transient behavior in regular diffusion and birth-death processes. Part IIJournal of Applied Probability, 1965
- A central limit theorem for processes defined on a finite Markov chainMathematical Proceedings of the Cambridge Philosophical Society, 1964