Research demonstrates a unified method for moment identities in Markov chains, implicating potential theory connections.
An occupation measure describes the expected amount of time a stochastic process spends in different parts of its state space prior to a given random time. It is shown that a basic identity involving occupation measures provides a unified approach to a variety of moment identities for Markov chains, and some connections with potential theory are made.
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Jim Pitman (1977) studied this question.
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