论文标题
在尺寸不同
Explicit heat kernels of a model of distorted Brownian motion on spaces with varying dimension
论文作者
论文摘要
在本文中，我们研究了具有不同维度的状态空间上的特定扭曲的布朗运动（DBM）模型。粗略地说，这样一个过程的状态空间由两个组成部分组成：$ 3 $维的组件和$ 1 $维的组件。这两个部分在起源时融为一体。 DBM在$ 3 $ - 或$ 1 $二维组件上的限制在对原点方面具有强烈的“推动”。在每个组件上，“推”的“大小”可以通过常数$γ> 0 $进行参数。在本文中，使用概率方法，我们获得了DBM的过渡密度函数的精确表达式，任何$ 0 <t <\ iftty $都具有不同的尺寸。
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 $1$-dimensional component. These two parts are joined together at the origin. The restriction of dBM on the $3$- or $1$-dimensional component receives a strong "push" towards the origin. On each component, the "magnitude" of the "push" can be parametrized by a constant $γ>0$. In this article, using probabilistic method, we get the exact expressions for the transition density functions of dBM with varying dimension for any $0<t<\infty$.
