Long-time behavior for a class of Feller processes (Q2787959)

The author provides a Chung-Fuchs type condition for the recurrence of a Feller process. The recurrence-transience property is widely studied in the literature for various classes of processes (see for instance [\textit{B. Franke}, Bernoulli 12, No. 3, 551--570 (2006); correction ibid. 13, No. 2, 600 (2007; Zbl 1114.60028)]).NEWLINENEWLINE Furthermore, the recurrence and transience are studied relative to the dimension of the state space, Pruitt indices and recurrence-transience of Feller-Dynkin diffusions and stable-like processes. Also, the perturbations of symbols, which will not affect the recurrence and transience of the underlying Feller processes are studied, along with sufficient conditions for the recurrence-transience in terms of the underlying Lévy measure.