A Consistent Markov Partition Process Generated from the Paintbox Process
نویسنده
چکیده
We study a family of Markov processes on P , the space of partitions of the natural numbers with at most k blocks. The process can be constructed from a Poisson point process on R+ ×∏ki=1 P (k) with intensity dt ⊗ (k) ν , where ν is the distribution of the paintbox based on the probability measure ν on Pm, the set of ranked-mass partitions of 1, and (k) ν is the product measure on ∏k i=1 P . We show that these processes possess a unique stationary measure, and we discuss a particular set of reversible processes for which transition probabilities can be written down explicitly.
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