Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-22T21:58:06.629Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of transient behaviour of certain processes with return to a central state

Published online by Cambridge University Press:  14 July 2016

Peter G. Buckholtz ,
L. Lorne Campbell ,
Ross D. Milbourne  and
M. T. Wasan
Peter G. Buckholtz*
Affiliation:
Royal Military College of Canada
L. Lorne Campbell*
Affiliation:
Queen's University
Ross D. Milbourne*
Affiliation:
Queen's University
M. T. Wasan*
Affiliation:
Queen's University
*
∗ Postal address: Department of Mathematics, Royal Military College of Canada, Kingston, Ontario, K7L 2W3, Canada.
∗∗ Postal address: Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, K7L 3N6, Canada.
∗∗∗ Postal address: Department of Economics, Queen's University, Kingston, Ontario, K7L 3N6, Canada.
∗∗ Postal address: Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, K7L 3N6, Canada.
Get access Rights & Permissions [Opens in a new window]

Abstract

In economics, cash management problems may be modelled by birth-death processes which reset to central states when a boundary is reached. The nature of the transient behaviour of the probability distribution of such processes symmetric about a central state is investigated. A diffusion approximation of such processes is given and the transient probability behaviour derived from the diffusion equation.

Keywords

BIRTH-DEATH WITH RETURNDIFFUSION WITH RETURN
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 1 , March 1983 , pp. 61 - 70
Copyright
Copyright © Applied Probability Trust 1983 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research supported by the Natural Sciences and Engineering Research Council of Canada.

References

[1] Buckholtz, P. and Wasan, M. T. (1981) Investigation of the critical nature of stochastic processes admitting diffusion approximations using Bernstein stochastic differentials. Selecta Statistica Canadiana 4, 45–94.Google Scholar
[2] Feller, W. (1954) Diffusion processes in one dimension. Trans. Amer. Math. Soc. 77, 1–31.CrossRefGoogle Scholar
[3] Milbourne, R. D. Optimal money holding under uncertainty and the demand for money. Queen's University Discussion Paper 372.Google Scholar
[4] Milbourne, R. D., Buckholtz, P. and Wasan, M. T. (1981) Cash balances as a random walk. Second Canadian Conference on Applied Statistics, Concordia University.Google Scholar
[5] Miller, M. H. and Orr, D. (1966) A model of the demand for money by firms. Quarterly J. Economics 80, 413–435.Google Scholar