Brownian motion with drift on spaces with varying dimension

被引：3

作者：

Lou, Shuwen ^{[1
]}

机构：

[1] Univ Toronto, Dept Stat Sci, Toronto, ON M5S 3G3, Canada

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2019年 / 129卷 / 06期

关键词：

Space of varying dimension; Brownian motion; Laplacian; Singular drift; Transition density function; Heat kernel estimates; Green function; OPERATORS;

D O I：

10.1016/j.spa.2018.07.001

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Many properties of Brownian motion on spaces with varying dimension (BMVD in abbreviation) have been explored in Chen and Lou (2018). In this paper, we study Brownian motion with drift on spaces with varying dimension (BMVD with drift in abbreviation). Such a process can be conveniently defined by a regular Dirichlet form that is not necessarily symmetric. Through the method of Duhamel's principle, it is established in this paper that the transition density of BMVD with drift has the same type of two-sided Gaussian bounds as that for BMVD (without drift). As a corollary, we derive Green function estimate for BMVD with drift. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：2086 / 2129

页数：44

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