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arXiv · 2209.14135

Non-local Boundary Value Problems, stochastic resetting and Brownian motions on graphs

Stefano Bonaccorsi·Fausto Colantoni·Mirko D'Ovidio·Gianni Pagnini
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Abstract

We consider dynamic boundary conditions involving non-local operators. Our analysis includes a detailed description of such operators together with their relations with random times and random (additive) functionals. We provide some new characterizations for the boundary behaviour of the Brownian motion based on the interplay between non-local operators and boundary value problems. Our main focus is on Feller-Wentzell diffusions with jumps (resetting/restart). We first consider the instructive case of the real line, then we extend our results on star graphs with trapping points or repulsive vertices.

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Stefano Bonaccorsi, Fausto Colantoni, Mirko D'Ovidio, Gianni Pagnini. 2022-09-28. Non-local Boundary Value Problems, stochastic resetting and Brownian motions on graphs. https://arxiv.org/abs/2209.14135

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