Brownian motion with drift on spaces with varying dimension

Shuwen Lou

Stochastic Processes and their Applications, 2019, vol. 129, issue 6, 2086-2129

Abstract: 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.

Keywords: Space of varying dimension; Brownian motion; Laplacian; Singular drift; Transition density function; Heat kernel estimates; Green function (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2018.07.001

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