On a Brownian motion conditioned to stay in an open set

Abstract

UDC 519.21

Distribution of a Brownian motion conditioned to start from the boundary of an open set $G$ and to stay in $G$ 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 $\mathbb{R}.$

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Published
22.09.2020
How to Cite
RiabovG. V. “On a Brownian Motion Conditioned to Stay in an Open Set”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 9, Sept. 2020, pp. 1286-03, doi:10.37863/umzh.v72i9.6281.
Section
Research articles