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June 2021 Explicit heat kernels of a model of distorted Brownian motion on spaces with varying dimension
Shuwen Lou
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Illinois J. Math. 65(2): 287-312 (June 2021). DOI: 10.1215/00192082-8939623

Abstract

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” toward the origin. On each component, the “magnitude” of a “push” can be parametrized by a constant γ>0. In this article, using the probabilistic method, we get the exact expressions for the transition density functions of dBM with varying dimension for any 0<t<.

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Shuwen Lou. "Explicit heat kernels of a model of distorted Brownian motion on spaces with varying dimension." Illinois J. Math. 65 (2) 287 - 312, June 2021. https://doi.org/10.1215/00192082-8939623

Information

Received: 24 January 2020; Revised: 12 November 2020; Published: June 2021
First available in Project Euclid: 9 April 2021

Digital Object Identifier: 10.1215/00192082-8939623

Subjects:
Primary: 60J60
Secondary: 60J35 , 60J45 , 60J65

Rights: Copyright © 2021 by the University of Illinois at Urbana–Champaign

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Vol.65 • No. 2 • June 2021
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