Working Paper Article Version 2 This version is not peer-reviewed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)

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

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

Comment 1
Commenter: Rafed MOUSSA
Commenter's Conflict of Interests: Author
Comment: New version of the manuscript with some corrections.
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