Some stochastic processes with absorbing barriers

Thomas Saaty
Joseph M. Katz Graduate School of Business
University of Pittsburgh
United States

Publication date: Jul, 1961

Journal: Journal of the Royal Statistical Society: Series B
Vol.: 23- Issue: 2- Pages: 319-334

Abstract: Models for growth distributions of biological organisms are investigated in this paper. They are specializations of the birth–death equations with two absorbing barriers. The solutions we seek are the distributions of the time to grow from an initial dose to an infective dose. Equations for these functions are simply obtained from the birth–death equations. Two main cases of interest are then examined. In the first case the birth and death rates are proportional to the number present and in the second case they are constant. Graphs are developed for the solution of the first case. Useful applications depend on this result.

Keywords: Stochastic problem, Growth distribution of biological organisms, Birth-death equations