论文标题
空间上的布朗尼运动扭曲的尺寸变化
Distorted Brownian motions on space with varying dimension
论文作者
论文摘要
粗略地说，具有不同维度的空间由至少两个具有不同尺寸的组件组成。在本文中，我们将专注于一个，可以将其视为$ \ mathbb {r}^3 $ tying ty ty ty ty ty ty not ty ty in the Origin the Origin的半行。目标是双重的。一方面，我们将在这个空间上引入所谓的扭曲的布朗尼动作，并具有不同的维度（缩写为dbmvds），并通过迪里奇特（Dirichlet）形式研究其基本特性。另一方面，我们将证明这些DBMVD的过渡密度函数的关节连续性，并得出它们的短时热核估计。
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 $\mathbb{R}^3$ at the origin. The aim is twofold. On one hand, we will introduce so-called distorted Brownian motions on this space with varying dimension (dBMVDs in abbreviation) and study their basic properties by means of Dirichlet forms. On the other hand, we will prove the joint continuity of the transition density functions of these dBMVDs and derive the short-time heat kernel estimates for them.
