English

On a Brownian motion conditioned to stay in an open set

Probability 2020-10-02 v1

Abstract

Distribution of a Brownian motion conditioned to start from the boundary of an open set GG and to stay in GG for a finite period of time is studied. Characterizations of such distributions in terms of certain singular stochastic differential equations are obtained. Results are applied to the study of boundaries of clusters in some coalescing stochastic flows on R.\mathbb{R}.

Keywords

Cite

@article{arxiv.2010.00260,
  title  = {On a Brownian motion conditioned to stay in an open set},
  author = {Georgii V. Riabov},
  journal= {arXiv preprint arXiv:2010.00260},
  year   = {2020}
}