A time-reversibility relationship between two Markov chains with exponential stationary distributions
- 1 March 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 25 (02) , 418-422
- https://doi.org/10.1017/s0021900200041061
Abstract
The stationary non-negative Markov chains {Yn } and {Xn } specified by the relations for {η n } a sequence of independent identically distributed (i.i.d.) random variables which are independent of {Yn }, and for {ξ n } a sequence of i.i.d. random variables which are independent of {Xn }, are mutually time-reversed if and only if their common marginal distribution is exponential, relating the exponential autoregressive process of Gaver and Lewis (1980) to the exponential minification process of Tavares (1980).Keywords
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