In this paper we prove the uniform boundary Harnack principle in general open sets for harmonic functions with respect to a large class of rotationally symmetric purely discontinuous Levy processes.
In this paper,we study the quasi-stationarity and quasi-ergodicity of general Markov processes.We show,among other things,that if X is a standard Markov process admitting a dual with respect to a finite measure m and ...In this paper,we study the quasi-stationarity and quasi-ergodicity of general Markov processes.We show,among other things,that if X is a standard Markov process admitting a dual with respect to a finite measure m and if X admits a strictly positive continuous transition density p(t,x,y)(with respect to m)which is bounded in(x,y)for every t>0,then X has a unique quasi-stationary distribution and a unique quasi-ergodic distribution.We also present several classes of Markov processes satisfying the above conditions.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12171335,11931004,12071011)the Science Development Project of Sichuan University(No.2020SCUNL201)the Simons Foundation(No.960480)。
基金supported by National Research Foundation of Korea (Grant No. 2011-0027230)supported in part by a grant from the Simons Foundation (Grant No. 208236)supportedin part by the MZOS Grant (Grant No. 037-0372790-2801)
文摘In this paper we prove the uniform boundary Harnack principle in general open sets for harmonic functions with respect to a large class of rotationally symmetric purely discontinuous Levy processes.
基金supported by National Natural Science Foundation of China(GrantNo.11171010)Beijing Natural Science Foundation(Grant No.1112001)
文摘In this paper,we study the quasi-stationarity and quasi-ergodicity of general Markov processes.We show,among other things,that if X is a standard Markov process admitting a dual with respect to a finite measure m and if X admits a strictly positive continuous transition density p(t,x,y)(with respect to m)which is bounded in(x,y)for every t>0,then X has a unique quasi-stationary distribution and a unique quasi-ergodic distribution.We also present several classes of Markov processes satisfying the above conditions.
