Let $B$ be a Brownian motion and $T_1$ its first hitting time of the level $1$. For $U$ a uniform random variable independent of $B$, we study in depth the distribution of $B_{UT_1}/sqrt{T_1}$, that is the rescaled Brownian motion sampled at uniform time. In particular, we show that this variable is centered.
展开▼
机译：假设$ B $是布朗运动，$ T_1 $是第1级水平的第一击中时间。对于$ U $，一个独立于$ B $的统一随机变量，我们深入研究$ B_ {UT_1} / sqrt {T_1} $的分布，即在统一时间采样的重新缩放的布朗运动。特别是，我们表明此变量居中。
展开▼
