We study the 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. The characterizations of distributions of this kind in terms of certain singular stochastic differential equations are obtained. The accumulated results are applied to the study of boundaries of the clusters in some coalescing stochastic flows on ℝ.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 9, pp. 1286–1303, September, 2020. Ukrainian DOI: 10.37863/umzh.v72i9.6281.
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Riabov, G.V. On a Brownian Motion Conditioned to Stay in an Open Set. Ukr Math J 72, 1482–1502 (2021). https://doi.org/10.1007/s11253-021-01866-6
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DOI: https://doi.org/10.1007/s11253-021-01866-6