Article
Version 2
This version is not peer-reviewed
Some Dirichlet Forms on Graphs as Traces of One-Dimensional Diffusions
Version 1
: Received: 31 May 2020 / Approved: 31 May 2020 / Online: 31 May 2020 (21:05:36 CEST)
Version 2 : Received: 11 August 2020 / Approved: 20 August 2020 / Online: 20 August 2020 (03:49:03 CEST)
Version 2 : Received: 11 August 2020 / Approved: 20 August 2020 / Online: 20 August 2020 (03:49:03 CEST)
How to cite: Moussa, R. Some Dirichlet Forms on Graphs as Traces of One-Dimensional Diffusions. Preprints 2020, 2020050513 Moussa, R. Some Dirichlet Forms on Graphs as Traces of One-Dimensional Diffusions. Preprints 2020, 2020050513
Abstract
We compute explicitly traces of one-dimensional diffusion processes. The obtained trace forms can be regarded as Dirichlet forms on graphs. Then we discuss conditions ensuring the trace forms to be conservative. Finally, the obtained results are applied to the one-dimensional diffusion related to the Bessel’s process of order $\nu$.
Keywords
Dirichlet forms; conservativeness; diffusion processes; graphs
Subject
Computer Science and Mathematics, Computer Vision and Graphics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Commenter: Rafed MOUSSA
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