34 citations · 260 across the 72 of their papers we have counts for
32 papers · 1 filter
On hitting time distributions of Markov processes with sub-Gaussian heat kernel bounds
Liping Li, Shuwen Lou
In this paper, we study the hitting times of Borel right processes on a metric measure space whose heat kernels satisfy sub-Gaussian bounds. It is well known that if $X=(…
On the restriction of a right process outside a negligible set
Liping Li, Michael Röckner
The objective of this paper is to examine the restriction of a right process on a Radon topological space, excluding a negligible set, and investigate whether the restricted object…
Dirichlet form approach to diffusions with discontinuous scale
Liping Li
It is well known that a regular diffusion on an interval without killing inside is uniquely determined by a canonical scale function and a canonical speed measure . Note…
On generalization of quasidiffusions
Liping Li
A quasidiffusion is by definition a time-changed Brownian motion on certain closed subset of . The aim of this paper is two-fold. On one hand, we will put forward a gen…
Fukushima subspaces of quasidiffusions
Liping Li, Jiangang Ying
Quasidiffusions are, by definition, time-changed Brownian motions on certain closed subset of . They admit an explicit representation of Dirichlet forms in terms of so-…
Ray-Knight compactification of birth and death processes
Liping Li
A birth and death process is a continuous-time Markov chain with the minimal state space , whose transition matrix is standard and whose density matrix is the given birt…
On diffusions with discontinuous scales
Liping Li
It is well known that a regular diffusion on an interval without killing inside is uniquely determined by a canonical scale function and a canonical speed measure . Note…
On structure of -harmonic functions for one-dimensional diffusions
Liping Li
In this note we analyse the harmonic functions in -sense for an irreducible diffusion on an interval.
Generalizing Dirichlet-to-Neumann operators
Liping Li
The aim of this paper is to study the Dirichlet-to-Neumann operators in the context of Dirichlet forms and especially to figure out their probabilistic counterparts. Regarding irre…
On trace of Brownian motion on the boundary of a strip
Liping Li, Wenjie Sun
The trace of a Markov process is the time changed process of the original process on the support of the Revuz measure used in the time change. In this paper, we will concentrate on…
On a stiff problem in two-dimensional space
Liping Li, Wenjie Sun
In this paper we will study a stiff problem in two-dimensional space and especially its probabilistic counterpart. Roughly speaking, the heat equation with a parameter $\varepsilon…
Hunt's hypothesis and symmetrization for general 1-dimensional diffusions
Liping Li
In this paper, we will consider the problem that how far from Hunt's hypothesis (H) to symmetrization for a general 1-dimensional diffusion. A characterization of (H) involving the…
Distorted Brownian motions on space with varying dimension
Liping Li, Shuwen Lou
Roughly speaking, a space with varying dimension consists of at least two components with different dimensions. In this paper we will concentrate on the one, which can be treated a…
Dirichlet forms and polymer models based on stable processes
Liping Li, Xiaodan Li
In this paper, we are concerned with polymer models based on -stable processes, where and stands for dimension. They are attached with a delta…
On general skew Brownian motions
Liping Li
The aim of this paper is two-fold. On one hand, we will study the distorted Brownian motion on , i.e. the diffusion process associated with a regular and strongly l…
Effective intervals and regular Dirichlet subspaces
Liping Li, Wenjie Sun, Jiangang Ying
It is shown in [10] that a regular and local Dirichlet form on an interval can be represented by so-called effective intervals with scale functions. This paper focuses on how to op…
Snapping out Walsh's Brownian motion and related stiff problem
Liping Li, Wenjie Sun
Firstly, we shall introduce the so-called snapping out Walsh's Brownian motion and present its relation with Walsh's Brownian motion. Then the stiff problem related to Walsh's Brow…
On stiff problems via Dirichlet forms
Liping Li, Wenjie Sun
The stiff problem is concerned with a thermal conduction model with a singular barrier of zero volume. In this paper, we shall build the phase transitions for the stiff problems in…
On the Dirichlet form of three-dimensional Brownian motion conditioned to hit the origin
Patrick J. Fitzsimmons, Liping Li
Our concern in this paper is the energy form induced by an eigenfunction of a self-adjoint extension of the restriction of the Laplace operator to $C_c^\infty(\mathbf{R}^3\setminus…
On symmetric one-dimensional diffusions
Liping Li, Jiangang Ying
The main purpose of this paper is to explore the structure of local and regular Dirichlet forms associated with symmetric linear diffusions. Let be a re…
The orthogonal complements of in its regular Dirichlet extensions
Yuncong Shen, Liping Li, Jiangang Ying
Consider the regular Dirichlet extension for one-dimensional Brownian motion, that is a subspace of and $\mathcal{E}(f,g…
Class of smooth functions in Dirichlet spaces
Patrick J. Fitzsimmons, Liping Li
Given a regular Dirichlet form on a fixed domain of , we first indicate that the basic assumption i…
Regular Dirichlet extensions of one-dimensional Brownian motion
Liping Li, Jiangang Ying
The regular Dirichlet extension is the dual concept of regular Dirichlet subspace. The main purpose of this paper is to characterize all the regular Dirichlet extensions of one-dim…
Criticality and subcriticality of generalized Schrödinger forms with non-local perturbations
Liping Li
In this paper, we shall treat the Schrödinger forms with non-local perturbations. We first extend the definitions of subcriticality, criticality and supercriticality for the Schröd…