Transience and Recurrence of Markov Processes with Constrained Local Time

Adam Barker (University of Reading)

Frank Adams 2,

We study the problem of a Markov process conditioned so that its local time must grow slower than a prescribed function. Building upon recent work on Brownian motion with constrained local time in [1], we study the problem for a large class of Markov processes. We find a necessary and sufficient condition for transience/recurrence of the conditioned process, and also explicitly determine the distributions of the conditioned (inverse) local time and the conditioned Markov process.

References:

[1] Kolb, M., Savov, M. Transience and recurrence of a Brownian path with limited local time. Ann. Probab. 44 (2016), no. 6, 4083--4132.

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