English

Analytic and stochastic description of Brownian motions on star graphs

Probability 2025-11-26 v1

Abstract

We provide a detailed description of all possible Feller processes on infinite} star graphs with finite number of edges, processes that while away from the graph's center behave like a one-dimensional Brownian motion. The description can be seen as a continuation of the seminal paper by It\^o and McKean (devoted to Brownian motions on the half-line), recast from the perspective of the theory of multi-armed bandits.

Keywords

Cite

@article{arxiv.2511.20039,
  title  = {Analytic and stochastic description of Brownian motions on star graphs},
  author = {Adam Bobrowski and Andrey Pilipenko},
  journal= {arXiv preprint arXiv:2511.20039},
  year   = {2025}
}

Comments

90 pages, 4 figures