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Brownian motion with drift on spaces with varying dimension

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  • Lou, Shuwen

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.

Suggested Citation

  • Lou, Shuwen, 2019. "Brownian motion with drift on spaces with varying dimension," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 2086-2129.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:6:p:2086-2129
    DOI: 10.1016/j.spa.2018.07.001
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    Cited by:

    1. Lou, Shuwen, 2023. "On transition density functions of skew Brownian motions with two-valued drift," Statistics & Probability Letters, Elsevier, vol. 193(C).

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