Stationary Infinitely-Divisible Markov Processes with Non-negative Integer Values
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چکیده
We characterize all stationary time-reversible Markov processes whose finite-dimensional marginal distributions (of all orders) are infinitely divisible. Aside from two trivial cases (iid and constant), every such process with full support in both discrete and continuous time is a branching process with Poisson or Negative Binomial marginal distributions and a specific bivariate distribution at pairs of times.
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تاریخ انتشار 2011