RIMS-1753 BOUNDARY HARNACK INEQUALITY FOR MARKOV PROCESSES WITH JUMPS By
نویسندگان
چکیده
We prove a boundary Harnack inequality for jump-type Markov processes on metric measure state spaces, under comparability estimates of the jump kernel and Urysohn-type property of the domain of the generator of the process. The result holds for positive harmonic functions in arbitrary open sets. It applies, e.g., to many subordinate Brownian motions, Lévy processes with and without continuous part, stable-like and censored stable processes, jump processes on fractals, and rather general Schrödinger, drift and jump perturbations of such processes.
منابع مشابه
Harnack Inequality for Some Classes of Markov Processes∗
In this paper we establish a Harnack inequality for nonnegative harmonic functions of some classes of Markov processes with jumps. AMS 2000 Mathematics Subject Classification: Primary 60J45, 60J75, Secondary 60J25.
متن کاملBoundary Harnack Inequality for Markov Processes with Jumps
We prove a boundary Harnack inequality for jump-type Markov processes on metric measure state spaces, under comparability estimates of the jump kernel and Urysohn-type property of the domain of the generator of the process. The result holds for positive harmonic functions in arbitrary open sets. It applies, e.g., to many subordinate Brownian motions, Lévy processes with and without continuous p...
متن کاملMathematische Zeitschrift Harnack inequality for some classes of Markov processes
In this paper we establish a Harnack inequality for nonnegative harmonic functions of some classes of Markov processes with jumps. Mathematics Subject Classification (2000): Primary 60J45, 60J75, Secondary 60J25.
متن کاملStochastic Differential Equations with Jumps
Gradient estimates and a Harnack inequality are established for the semigroup associated to stochastic differential equations driven by Poisson processes. As applications, estimates of the transition probability density, the compactness and ultraboundedness of the semigroup are studied in terms of the corresponding invariant measure.
متن کاملParabolic Harnack inequality and heat kernel estimates for random walks with long range jumps
We investigate the relationships between the parabolic Harnack inequality, heat kernel estimates, some geometric conditions, and some analytic conditions for random walks with long range jumps. Unlike the case of diffusion processes, the parabolic Harnack inequality does not, in general, imply the corresponding heat kernel estimates.
متن کامل