Fangyuan Lin L&S Math & Physical Sciences
When is a Function of a Markov Process Markov?
“A fundamental question that continually reappears in the study of Markov processes is, “When is a function of a Markov process also a Markov process?” A classical and somewhat obvious criterion was supplied by (Dynkin, 1965). Dynkin’s result gives a sufficient condition for such a state of affairs to hold for an arbitrary starting state. A much more subtle and general criterion involving the novel notion of intertwining of kernels was presented in (Rogers & Pitman, 1981). A key observation of this paper is that Markovianity may only hold for a restricted family of initial distributions.
The specific question that my research project asks is: What are the many and varied instances and discrete time analogues of Theorem 2 of the 1981 paper Markov functions by Rogers and Pitman that have appeared in the literature since it was published? My project may also uncover new insights about the conditions that are sufficient to ensure that a function of a time-homogeneous Markov process is again a time-homogeneous Markov process.”
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