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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.
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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 

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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