On the conservativeness and the recurrence of symmetric jump-diffusions

By J. Masamune, T. Uemura, Jian Wang. 2012

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Abstract Sufficient conditions for a symmetric jump-diffusion process to be conservative and recurrent are given in terms of the volume of the state space and the jump kernel of the process. A number of examples are presented to illustrate the optimality of these conditions; in particular, the situation is allowed to be that the state space is topologically disconnected but the particles can jump from a connected component to the other components.

Subfields: Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/234fffbcce580845ed40d0faccdc6dc70dfaf70d