Probability in the Engineering and Informational Sciences

Table of Contents - 1994 - Volume 8, Issue 01  

Research Article

Bounds for Stopping Times with Application to the Approximation of Distribution Functions

Rhonda Richtera1 and J. George Shanthikumara2*

a1 Department of Decision and Information Sciences, Santa Clara University, Santa Clara, California 95053

a2 Walter A. Haas School of Business, University of California at Berkeley, Berkeley, California 94720

Abstract

We consider stopping times associated with sequences of non-negative random variables and Poisson processes. With sufficient conditions on the dependence property between the sequences of non-negative random variables (or the Poisson processes) and the stopping times, we develop easily computable stochastic bounds for the stopping times. We use these bounds to develop approximations within the class of generalized phase-type distribution functions for arbitrary distribution functions. The computational tractability of generalized phase-type distribution functions facilitate the computational analysis of complex stochastic systems using these approximate distribution functions. Applications of these approximations to renewal processes are illustrated.

Footnotes

* Supported in part by NSF grant DDM-9113008.