Lower escape rate of symmetric jump-diffusion processes (Q2786456)

In [Appl. Anal. 71, No. 1--4, 63--89 (1999; Zbl 1020.58024)], \textit{A. Grigor'yan} provided an integral test for the lower escape rate of Brownian motions on Riemann manifolds. The author generalizes this result to symmetric jump-diffusion processes generated by regular Dirichlet forms. It turns out that the scaling order of big jumps determines the speed of particles escaping to infinity. The approach is similar to Grigor'yan's: first an upper estimate for the probability of hitting a compact set after a fixed time is given in terms of the capacity, see [\textit{A. Bendikov} and \textit{L. Saloff-Coste}, Osaka J. Math. 42, No. 3, 677--722 (2005; Zbl 1085.31007)]. Then, a capacity upper estimate for Dirichlet forms of non-local type is used, see [\textit{H. Ôkura}, Potential Anal. 19, No. 3, 211--235 (2003; Zbl 1039.31011)]. The test is applied to symmetric jump processes of variable order. Finally, upper and lower escape rates of time-changed processes are derived, using the rates of the underlying processes.