论文标题
在二维中厚点的紧密度
Tightness for Thick Points in two dimensions
论文作者
论文摘要
令$ w_ {t} $在飞机上开始时是布朗尼运动，让$θ$为单位磁盘$ d_ {1} $的第一个退出时间。让 \ [μ_{θ}（x，ε）= \ frac {1} {πε^{2}}} \ int_ {0}^{θ}}^{θ} 1 _ {\ {b（x，x，ε）\}}}}}}（w_ {t}）（w_ {t}） θ}（ε）= \ sup_ {x \ in d_ {1}}}μ_{θ}（x，ε）$。我们表明\ [\ sqrt {μ^{\ ast}_θ（ε）} - \ sqrt {2/π} \ left（\logε^{ - 1} - \ frac {1} {1} {2} {2} {2} \ log \ log \ log \ε^{ - 1}} \ right）
Let $W_{t}$ be Brownian motion in the plane started at the origin and let $ θ$ be the first exit time of the unit disk $D_{1}$. Let \[μ_{ θ} ( x,ε) =\frac{1}{πε^{ 2} }\int_{0}^{ θ}1_{\{ B( x,ε)\}}( W_{t})\,dt,\] and set $μ^{ \ast}_{ θ} (ε)=\sup_{x\in D_{1}}μ_{ θ} ( x,ε)$. We show that \[\sqrt{μ^{\ast}_θ (ε)}-\sqrt{2/π} \left(\log ε^{-1}- \frac{1}{2}\log\log ε^{-1}\right)\] is tight.
