7 citations · 16 across the 13 of their papers we have counts for
15 papers · 1 filter
Heat kernel estimates for Markov processes in bounded sets with jump kernels decaying at the boundary
Soobin Cho, Panki Kim, Renming Song +1
In this paper, we study two types of purely discontinuous symmetric Markov processes in bounded smooth subsets of : conservative processes and processes killed eit…
Heat kernel estimates for Markov processes with blowing-up jump kernels
Soobin Cho, Panki Kim, Renming Song +1
In this paper, we establish sharp two-sided heat kernel estimates for a large class of purely discontinuous symmetric Markov processes on closed subsets of , whos…
Approximate factorizations for non-symmetric jump processes
Soobin Cho, Renming Song
In this paper, we first extend the approximate factorization for purely discontinuous Markov process established in \cite{CKSV20} by getting rid of some of the conditions imposed i…
Heat kernel estimates for Schrödinger operators with supercritical killing potentials
Soobin Cho, Panki Kim, Renming Song
In this paper, we study the Schrödinger operator , where is a supercritical non-negative potential belonging to a large class of functions containing functions of the form…
Fractional Laplacian with supercritical killings
Soobin Cho, Renming Song
In this paper, we study Feynman-Kac semigroups of symmetric -stable processes with supercritical killing potentials belonging to a large class of functions containing functions…
Markov processes with jump kernels decaying at the boundary
Soobin Cho, Panki Kim, Renming Song +1
The goal of this work is to develop a general theory for non-local singular operators of the type $$ L^{\mathcal{B}}_αf(x)=\lim_{ε\to 0} \int_{D,\, |y-x|>ε}\big(f(y)-f(x)\big) \mat…
Laws of the iterated logarithm for occupation times of Markov processes
Soobin Cho, Panki Kim, Jaehun Lee
In this paper, we discuss the laws of the iterated logarithm (LIL) for occupation times of Markov processes in general metric measure space both near zero and near infinity und…
Heat kernel estimates for Dirichlet forms degenerate at the boundary
Soobin Cho, Panki Kim, Renming Song +1
The goal of this paper is to establish sharp two-sided estimates on the heat kernels of two types of purely discontinuous symmetric Markov processes in the upper half-space of $\ma…
General Law of iterated logarithm for Markov processes: Liminf laws
Soobin Cho, Panki Kim, Jaehun Lee
Continuing from arXiv:2102.01917v2, in this paper, we discuss general criteria and forms of liminf laws of iterated logarithm (LIL) for continuous-time Markov processes. Under some…
Heat kernel estimates for subordinate Markov processes and their applications
Soobin Cho, Panki Kim, Renming Song +1
In this paper, we establish sharp two-sided estimates for transition densities of a large class of subordinate Markov processes. As applications, we show that the parabolic Harnack…
General Law of iterated logarithm for Markov processes: Limsup law
Soobin Cho, Panki Kim, Jaehun Lee
In this paper, we discuss general criteria of limsup law of iterated logarithm (LIL) for continuous-time Markov processes. We consider minimal assumptions for LILs to hold at zero(…
Estimates on transition densities of subordinators with jumping density decaying in mixed polynomial orders
Soobin Cho, Panki Kim
In this paper, we discuss estimates on transition densities for subordinators, which are global in time. We establish the sharp two-sided estimates on the transition densities for…
Estimates on the tail probabilities of subordinators and applications to general time fractional equations
Soobin Cho, Panki Kim
In this paper, we study estimates on tail probabilities of several classes of subordinators under mild assumptions on the tail of its Lévy measure. As an ap…
Estimates of Dirichlet heat kernels for unimodal Lévy processes with low intensity of small jumps
Soobin Cho, Jaehoon Kang, Panki Kim
In this paper, we study transition density functions for pure jump unimodal Lévy processes killed upon leaving an open set . Under some mild assumptions on the Lévy density, we…
Factorization and estimates of Dirichlet heat kernels for non-local operators with critical killings
Soobin Cho, Panki Kim, Renming Song +1
In this paper we discuss non-local operators with killing potentials, which may not be in the standard Kato class. We first discuss factorization of their Dirichlet heat kernels in…