布朗运动的跨度

IF 1.2 2区数学 Q2 STATISTICS & PROBABILITY

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2015-06-05 DOI:10.1214/16-AIHP749

S. Evans, J. Pitman, Wenpin Tang

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引用次数: 1

摘要

作者:Evans, s;皮特曼,J;摘要:©庞加莱研究所出版协会，2017。对于d λ{1,2,3}，令(Bdt;它是一个d维标准布朗运动。我们研究了d-布朗张成集span (d):= {t - s;Bds = Bdt，对于一些0 l l s l t}。我们几乎肯定地证明了随机集Span(d)在h +上是α-紧密的。此外，我们证明了Span(1)几乎肯定地= 1 +;Span(2)的Lebesgue测度几乎肯定为0，其Hausdorff维数几乎肯定为1;Span(3)的Hausdorff维数几乎肯定是12。我们还列出了一些猜想和尚未解决的问题。

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The spans in Brownian motion

Author(s): Evans, S; Pitman, J; Tang, W | Abstract: © Association des Publications de l'Institut Henri Poincare, 2017. For d ϵ {1, 2, 3}, let (Bdt ; t g 0) be a d-dimensional standard Brownian motion. We study the d-Brownian span set Span(d) := {t - s;Bds = Bdt for some 0 l s l t}. We prove that almost surely the random set Span(d) is α-compact and dense in ℝ+. In addition, we show that Span(1) = ℝ+ almost surely; the Lebesgue measure of Span(2) is 0 almost surely and its Hausdorff dimension is 1 almost surely; and the Hausdorff dimension of Span(3) is 12 almost surely. We also list a number of conjectures and open problems.

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来源期刊

Annales De L Institut Henri Poincare-probabilites Et Statistiques 数学-统计学与概率论

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Probability and Statistics section of the Annales de l’Institut Henri Poincaré is an international journal which publishes high quality research papers. The journal deals with all aspects of modern probability theory and mathematical statistics, as well as with their applications.