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Absorbing process in recursive stochastic equations

Part of: Stochastic systems and control Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Toshinao Nakatsuka
Toshinao Nakatsuka*
Affiliation:
Tokyo Metropolitan University
*
∗Postal address: Faculty of Economics, Tokyo Metropolitan University, 192–0397 Tokyo, Japan. E-mail address: tnaka@bcomp.metro-u.ac.jp
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Abstract

We introduce the concept of the absorbing process for analysing a state process. Our aim is to show the existence of the absorbing process with probability one. This process is shown to be stationary, asymptotically stationary, periodic or a.m.s., if the input distribution has such properties. The real process is absorbed into this process so that its stability and some other properties are easily derived.

Keywords

Absorbing processnon-stationaritystationarityasymptotic mean stationarityqueueing system

MSC classification

Primary: 93E15: Stochastic stability
Secondary: 60G17: Sample path properties
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 2 , June 1998 , pp. 418 - 426
Copyright
Copyright © Applied Probability Trust 1998 

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References

Bauer, H. (1981). Probability Theory and Elements of Measure Theory. Academic Press, New York.Google Scholar
Brandt, A., Franken, P., and Lisek, B. (1990). Stationary Stochastic Models. John Wiley & Sons, New York.Google Scholar
Gray, R.M., and Kieffer, J.C. (1980). Asymptotically mean stationary measures. Ann. Prob. 8, 962–973.Google Scholar
Krengel, U. (1985). Ergodic Theorems. Walter de Gruyter, Berlin.Google Scholar
Matthes, K., Kerstan, J., and Mecke, J. (1978). Infinitely Divisible Point Processes. John Wiley & Sons, New York.Google Scholar
Rolski, T. (1981). Queues with non-stationary input stream: Ross's conjecture. Adv. Appl. Prob. 13, 603–618.CrossRefGoogle Scholar
Szczotka, W. (1986). Stationary representation of queues I. Adv. Appl. Prob. 18, 815–848.CrossRefGoogle Scholar
Thorisson, H. (1985). On regenerative and ergodic properties of the k-server queue with non-stationary Poisson arrivals. J. Appl. Prob. 22, 893–902.Google Scholar