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2022 Distorted Brownian motions on space with varying dimension
Liping Li, Shuwen Lou
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Electron. J. Probab. 27: 1-32 (2022). DOI: 10.1214/22-EJP796


In this paper we introduce and study distorted Brownian motion on state spaces with varying dimension (dBMV in abbreviation). Roughly speaking, the state space of dBMV is embedded in R4 and consists of two components: a 3-dimensional component and a 1-dimensional component. These two parts are joined together at the origin. 3-dimensional dBMV models homopolymer with attractive potential at the origin and has been studied in [9], [8], [7]. dBMV restricted on the 1-dimensional component can be viewed as a Brownian motion with drift of Kato-class type. Such a process with varying dimensional can be concisely characterized in terms of Dirichlet forms. Using the method of radial process developed in [5] combined with some calculation specifically for dBMV, we get its short-time heat kernel estimates.

Funding Statement

The first named author is partially supported by NSFC (No. 11688101 and No. 11801546) and Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences (No. 2008DP173182).


Download Citation

Liping Li. Shuwen Lou. "Distorted Brownian motions on space with varying dimension." Electron. J. Probab. 27 1 - 32, 2022.


Received: 11 May 2021; Accepted: 15 May 2022; Published: 2022
First available in Project Euclid: 15 June 2022

Digital Object Identifier: 10.1214/22-EJP796

Primary: 60J45 , 60J46 , 60J60 , 60J65

Keywords: Dirichlet forms , distorted Brownian motions , Heat kernel estimates , varying dimension


Vol.27 • 2022
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