Research Reports from the Department of Operations
Document Type
Report
Publication Date
1-1-1970
Abstract
In [5] the homogeneous process X(t) defined on a finite irreducible Markov chain P(t) was studied. The process was characterized by an overall transition rate v per unit time, and P the matrix of transition probabilities for the chain and a linear growth for X(t) dependent on the chain; viz. d/dt X(t) = v•. The central limit behavior of the process was exhibited in [5]. For the case when the chain had only two states, the ruin and ergodic problems were considered in [4] for the bounded process. The object of this paper is to investigate the ruin and ergodic problems for the process of [5] in the presence of boundaries. We repeat the description of the process. Our interest lies in the two dimensional Markov process {X(t), R(t)} where --∞
Keywords
Operations research, Ergodic theory, Markov processes, Stochastic processes, Boundary value problems, Mathematical models
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 174
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Keilson, Julian and Subba Rao, S., "A Process with Chain Dependent Growth Rate - Part II The Ruin and Ergodic Problems" (1970). Research Reports from the Department of Operations. 441.
https://commons.case.edu/wsom-ops-reports/441