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.

中文翻译：

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关于有条件的布朗运动，要保持在开放状态

我们研究了一个布朗运动的分布，该运动的条件是从一个开放集G的边界开始，并在有限的一段时间内停留在G中。得到了根据某些奇异随机微分方程的这种分布特征。累积的结果被用于研究ℝ上的一些凝聚随机流中的簇的边界。