Shuwen Lou
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View article: Explicit Transition Density Functions of Skew Brownian Motions with Two-Valued Drift
Explicit Transition Density Functions of Skew Brownian Motions with Two-Valued Drift Open
In this article, we derive the explicit transition density functions of skew Brownian motion (SBM in abbreviation) with two-valued drift for all $t>0$. As an important step of this result, it is also shown in this paper that SBM with two-v…
View article: Discrete Approximation to Brownian Motion with Darning
Discrete Approximation to Brownian Motion with Darning Open
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, while it behaves like a regular BM outside of this area. In …
View article: Discrete approximation to Brownian motion with varying dimension in unbounded domains
Discrete approximation to Brownian motion with varying dimension in unbounded domains Open
We establish the discrete approximation to Brownian motion with varying dimension (BMVD in abbreviation) by random walks. The setting is very similar to that in [11], but here we use a different method allowing us to get rid the restrictio…
View article: Distorted Brownian motions on space with varying dimension
Distorted Brownian motions on space with varying dimension Open
In this paper we introduce and study distorted Brownian motion on state spaces with varying dimension (dBMV in abbreviation). Roughly speaking, the state space of dBMV is embedded in R4 and consists of two components: a 3-dimensional compo…
View article: Discrete Approximation to Brownian Motion with Varying Dimension in Unbounded Domains
Discrete Approximation to Brownian Motion with Varying Dimension in Unbounded Domains Open
We establish the discrete approximation to Brownian motion with varying dimension (BMVD in abbreviation) by random walks. The setting is very similar to that in [11], but here we use a different method allowing us to get rid the restrictio…
View article: Distorted Brownian motions on space with varying dimension
Distorted Brownian motions on space with varying dimension Open
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 as $\mathbb{R}^3$ tying a half line not contained by $\mathb…
View article: Discrete Approximation to Brownian Motion with Varying Dimension in Bounded Domains
Discrete Approximation to Brownian Motion with Varying Dimension in Bounded Domains Open
In this paper we study the discrete approximation to Brownian motion with varying dimension (BMVD in abbreviation) introduced in [4] by continuous time random walks on square lattices. The state space of BMVD contains a $2$-dimensional com…
View article: Explicit heat kernels of a model of distorted Brownian motion on spaces with varying dimension
Explicit heat kernels of a model of distorted Brownian motion on spaces with varying dimension Open
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 of two components: a $3$-dimensional component and a $1$-dim…
View article: Brownian motion on some spaces with varying dimension
Brownian motion on some spaces with varying dimension Open
In this paper, we introduce and study Brownian motion on a class of state spaces with varying dimension. Starting with a concrete case of such state spaces that models a big square with a flag pole, we construct a Brownian motion on it and…
View article: Brownian Motion with Drift on Spaces with Varying Dimension
Brownian Motion with Drift on Spaces with Varying Dimension Open
Many properties of Brownian motion on spaces with varying dimension (BMVD in abbreviation) have been explored in [5]. In this paper, we study Brownian motion with drift on spaces with varying dimension (BMVD with drift in abbreviation). Su…
View article: On-diagonal Heat Kernel Lower Bound for Strongly Local Symmetric Dirichlet Forms
On-diagonal Heat Kernel Lower Bound for Strongly Local Symmetric Dirichlet Forms Open
This paper studies strongly local symmetric Dirichlet forms on general measure spaces. The underlying space is equipped with the intrinsic metric induced by the Dirichlet form, with respect to which the metric measure space does not necess…
View article: Brownian Motion on Spaces with Varying Dimension
Brownian Motion on Spaces with Varying Dimension Open
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 pole, we construct a Brownian motion on it and study how h…
View article: Local times of stochastic differential equations driven by fractional Brownian motions
Local times of stochastic differential equations driven by fractional Brownian motions Open
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 in one dimension and in the rough case H<1/2, the Hölder e…
View article: Fractal Dimensions of Rough Differential Equations Driven by Fractional Brownian Motions
Fractal Dimensions of Rough Differential Equations Driven by Fractional Brownian Motions Open
In this work we study fractal properties of rough differential equations driven by a fractional Brownian motions with Hurst parameter $H>\frac{1}{4}$. In particular, we show that the Hausdorff dimension of the sample paths of the solution …