Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T01:24:27.107Z Has data issue: false hasContentIssue false
  • English
  • Français

On the stationary distribution of some extremal Markovian sequences

Published online by Cambridge University Press:  14 July 2016

M. T. Alpuim  and
E. Athayde
M. T. Alpuim
Affiliation:
University of Lisbon and CEA (INIC)
E. Athayde*
Affiliation:
University of Lisbon and CEA (INIC)
*
∗Postal address for both authors: DEIOC, University of Lisbon, 58 Rua da Escola Politécnica, 1294 Lisboa Codex, Portugal.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is concerned with the Markovian sequence Xn = Zn max{Xn–1, Yn},n ≧ 1, where X0 is any random variable, {Zn} and {Yn} are independent sequences of i.i.d. random variables both independent of X0. We consider the problem of characterizing the class of stationary distributions arising in such a model and give criteria for a d.f. to belong to it. We develop further results when the Zn's are random variables concentrated on the interval [0, 1], namely having a beta distribution.

Keywords

LIMIT DISTRIBUTIONBETA DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 291 - 302
Copyright
Copyright © Applied Probability Trust 1990 

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.)

References

Alpuim, M. T. (1989) An extremal Markovian sequence. J. Appl. Prob. 26, 219–232.Google Scholar
Chung, K. L. and Fuchs, W. H. J. (1951) On the distribution of values of sums of random variables. Mem. Amer. Math. Soc. 6, 1–12.Google Scholar
Daley, D. J. and Haslett, J. (1982) A thermal energy storage process with controlled input. Adv. Appl. Prob. 14, 257–271.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. II. Wiley, New York.Google Scholar
Haslett, J. (1979) Problems in the stochastic storage of a solar thermal energy. In Analysis and Optimization of Stochastic Systems, ed. Jacobs, O. Academic Press, London.Google Scholar
Helland, I. S. and Nilsen, T. S. (1976) On a general random exchange model J. Appl. Prob. 13, 781–790.Google Scholar
Hooghiemstra, G. and Keane, M. (1985) Calculation of the equilibrium distribution for a solar energy storage model J. Appl. Prob. 22, 852–864.Google Scholar
Hooghiemstra, G. and Scheffer, C. L. (1986) Some limit theorems for an energy storage model. Stoch. Proc. Appl. 22, 121–127.Google Scholar
Todorovic, P. and Gani, J. (1987) Modeling the effect of erosion on crop production. J. Appl. Prob. 24, 787–797.CrossRefGoogle Scholar