布朗运动被限制在一个锥体上

Q2 Mathematics

Journal of Mathematics of Kyoto University Pub Date : 2008-11-25 DOI:10.1215/KJM/1260975039

Rodolphe Garbit

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引用次数: 16

摘要

R. Durrett, D. Iglehart和D. Miller的结果表明，布朗弯曲是布朗运动在单位时间内被限制为正的，从某种意义上说，它是弱极限，当$x$趋于$0$时，布朗运动从$x$开始，并被限制为在单位时间内保持正。我们将这个极限定理推广到条件为停留在光滑凸锥上的多维布朗运动。

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Brownian motion conditioned to stay in a cone

A result of R. Durrett, D. Iglehart and D. Miller states that Brownian meander is Brownian motion conditioned to stay positive for a unit of time, in the sense that it is the weak limit, as $x$ goes to $0$, of Brownian motion started at $x>0$ and conditioned to stay positive for a unit of time. We extend this limit theorem to the case of multidimensional Brownian motion conditioned to stay in a smooth convex cone.

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来源期刊

Journal of Mathematics of Kyoto University 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

期刊介绍： Papers on pure and applied mathematics intended for publication in the Kyoto Journal of Mathematics should be written in English, French, or German. Submission of a paper acknowledges that the paper is original and is not submitted elsewhere.