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An exponential Markovian stationary process

Published online by Cambridge University Press:  14 July 2016

L. Valadares Tavares
L. Valadares Tavares*
Affiliation:
Technical University of Lisbon, IST
*
∗Postal address: CESUR — IST, Av. Rovisco Pais, 1000 Lisbon, Portugal. Research sponsored by the National Institute for Scientific Research (INIC).
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Abstract

A new markovian process {Xi : i = 0, 1, 2, ·· ·} following a negative exponential distribution and with the same autocorrelation function as the lag-1 autoregressive process is proposed and studied in this paper. The exact distribution of the maxima and of the minima of n consecutive Xi values are obtained and the exact expected upcrossing interval is given for any crossing level.

Keywords

NON-GAUSSIAN PROCESSEXTREMES DISTRIBUTIONUPCROSSING INTERVALS
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980 , pp. 1117 - 1120
Copyright
Copyright © Applied Probability Trust 

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References

Valadares Tavares, L. (1977) The exact distribution of extremes of a non-gaussian process. Stoch. Proc. Appl. 5, 151–156.CrossRefGoogle Scholar