Abstract
Under a slight regularity condition we prove that if the spent and residual waiting times at $t$ in a renewal process are independent random variables for one value of $t = t_0$, then the process is Poisson.
Citation
K. Bruce Erickson. Harry Guess. "A Characterization of the Exponential Law." Ann. Probab. 1 (1) 183 - 185, February, 1973. https://doi.org/10.1214/aop/1176997035
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