Open AccessOn a Brownian motion conditioned to stay in an open set
Author(s) -
Georgii Riabov
Publication year - 2020
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v72i9.6281
Subject(s) - brownian motion , stochastic differential equation , mathematics , brownian excursion , geometric brownian motion , boundary (topology) , motion (physics) , open set , reflected brownian motion , set (abstract data type) , mathematical analysis , diffusion process , local time , wiener process , statistical physics , classical mechanics , computer science , physics , statistics , pure mathematics , knowledge management , innovation diffusion , programming language
UDC 519.21Distribution of a Brownian motion conditioned to start from the boundary of an open set and to stay in 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