Elastic Brownian motion with random jumps from the boundary
Probability
2025-11-04 v1 Analysis of PDEs
Abstract
In this paper, we study elastic Brownian motion on a domain. Instead of being killed at the boundary, the process restarts from a random position inside the domain. We characterize this process through its stochastic differential equation (SDE), its generator, and a description of the paths. We also derive the invariant probability measure and the spectral representation. At the end, we focus on the harmonic functions on the upper half-space to study the trace process.
Keywords
Cite
@article{arxiv.2511.01455,
title = {Elastic Brownian motion with random jumps from the boundary},
author = {Fausto Colantoni and Mirko D'Ovidio},
journal= {arXiv preprint arXiv:2511.01455},
year = {2025}
}