BOUNDARY HARNACK INEQUALITY FOR MARKOV PROCESSES WITH JUMPS

作者：Bogdan Krzysztof^*; Kumagai Takashi; Kwasnicki Mateusz

来源：Transactions of the American Mathematical Society, 2015, 367(1): 477-517.

• Boundary Harnack inequality
• jump Markov process

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, Levy processes with and without continuous part, stable-like and censored stable processes, jump processes on fractals, and rather general Schrodinger, drift and jump perturbations of such processes.

• 出版日期2015-1