6 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=(…
Discrete Approximation to Brownian Motion with Darning
Shuwen Lou
Brownian motion with darning (BMD in abbreviation) is introduced and studied in [4] and [5, Chapter 7]. Roughly speaking, BMD travels across the "darning area" at infinite speed, w…
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…
Explicit heat kernels of a model of distorted Brownian motion on spaces with varying dimension
Shuwen Lou
In this paper, we study a particular model of distorted Brownian motion (dBM) on state spaces with varying dimension. Roughly speaking, the state space of such a process consists o…
Brownian Motion on Spaces with Varying Dimension
Zhen-Qing Chen, Shuwen Lou
In this paper we introduce and study Brownian motion on state spaces with varying dimension. Starting with a concrete case of such state spaces that models a big square with a flag…
Local times of stochastic differential equations driven by fractional Brownian motions
Shuwen Lou, Cheng Ouyang
In this paper, we study the existence and (Hölder) regularity of local times of stochastic differential equations driven by fractional Brownian motions. In particular, we show that…