On zeros of Martin-Löf random Brownian motion
On zeros of Martin-Löf random Brownian motion
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关于 Martin-Löf 随机布朗运动的零点
DOI：
10.4115/jla.2014.6.9
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
T. Slaman
中科院分区：
文献类型：
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作者：
L. Bienvenu;Kelty Allen;T. Slaman
我们研究了Martin-LOF随机布朗运动的样品路径特性。我们表明（1）许多经典的结果几乎可以肯定地持续到每一个随机布朗路径；相反，每个具有有效维度大于1/2的真实尺寸都必须是某些Martin-LOF随机Brownian路径的零，并且（3）我们将证明一个新的证据，表明平面中对Dirichlet问题的解决方案是可计算的。
We investigate the sample path properties of Martin-Lof random Brownian motion. We show (1) that many classical results which are known to hold almost surely hold for every Martin-Lof random Brownian path, (2) that the effective dimension of zeroes of a Martin-Lof random Brownian path must be at least 1/2, and conversely that every real with effective dimension greater than 1/2 must be a zero of some Martin-Lof random Brownian path, and (3) we will demonstrate a new proof that the solution to the Dirichlet problem in the plane is computable.