Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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 (doi: 10.20944/preprints202005.0513.v1). Moussa, R. Some Dirichlet Forms on Graphs as Traces of One-Dimensional Diffusions. Preprints 2020, 2020050513 (doi: 10.20944/preprints202005.0513.v1).

## Abstract

We compute explicitly trace of one-dimensional diffusion process which can be regarded as a Dirichlet form on graphs and we study its conservativeness property. Finally, we give an example of a discretization of one dimensional diffusion of Bessel's process with order $\nu$.

## Subject Areas

Dirichlet forms; trace operator; diffusion processes; Sturm-Liouville problem

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