An exponential Markovian stationary process

Abstract

A new markovian process {X i : 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.