R. Song

collaborators

4 papers

math.PR2025

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…

math.PR2025

Potential theory of Dirichlet forms with jump kernels blowing up at the boundary

Panki Kim, Renming Song, Zoran VondraÄek

In this paper we study the potential theory of Dirichlet forms on the half-space $R_{+}^{d}$ defined by the jump kernel $J (x, y) = ∣ x - y ∣^{- d - I^\pm} B (x, y)$ and the killing…

math.PR2024

Heat kernel estimates for regional fractional Laplacians with multi-singular critical potentials in $C^{1, I^^{2}}$ open sets

Renming Song, Peixue Wu, Shukun Wu

Let $D$ be an open set of $R^{d}$ , $I^\pm \in (0, 2)$ and let $L_{I^} \pm^{D}$ be the generator of the censored $I^\pm$ -stable process in $D$ . In this paper, we establish sharp t…

math.PR2024

Peixue Wu, Zhiwei Yang, Hong Wang +1

In this paper we introduce a variable order time fractional differential equation driven by pure jump LÃ©vy noise, which models the motion of a particle exhibiting memory effect. W…

Heat kernel estimates for Dirichlet forms degenerate at the boundary

Potential theory of Dirichlet forms with jump kernels blowing up at the boundary

Heat kernel estimates for regional fractional Laplacians with multi-singular critical potentials in C1,I^2 open sets

Time fractional stochastic differential equations driven by pure jump LÃ©vy noise

Heat kernel estimates for regional fractional Laplacians with multi-singular critical potentials in $C^{1, I^^{2}}$ open sets