engleski

Stochastic stability of Lévy-type processes

In this talk, we discuss transience, recurrence, weak and strong transience, and ergodicity of Feller processes associated with pseudo-differential operators - the so-called L\'evy-type processes. First, we present Chung-Fuchs type conditions for the transience and recurrence in terms of the symbol of the corresponding pseudo- differential operator. Next, by using these conditions we discuss the transience and recurrence with respect to the dimension of the state space and Pruitt indices, and the transience and recurrence of Feller- Dynkin diffusions and stable-like processes. In the one and two- dimensional cases, we analyze perturbations of these processes which do not affect their transience and recurrence properties, and we present sufficient conditions for their transience and recurrence in terms of the corresponding L\'evy measure. At the end, we introduce the notion of weak and strong transience and discuss ergodicity of L\'evy-type processes.

Feller process ; Feller-Dynkin diffusion ; Levy measure ; Pruitt indices ; recurrence ; stable-like process ; symbol ; transience

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