论文标题
贝塞尔过程的最后一个零弧形定律独立分解了漂移
Independent factorization of the last zero arcsine law for Bessel processes with drift
论文作者
论文摘要
我们表明，在$ 0 $ $ 0 $开始的时间$ t之前的最后一个时间$ t $ t $的分布与独立权利审查的指数随机变量和beta随机变量的分布相同。这扩展了Brownian Motion的Schulte-Geers和Stadje（2017）的最新结果，并随着漂移而逐渐流动。我们的证明是直观和直接的，同时避免了重型计算。为此，我们为贝塞尔工艺的平方进行了一种新颖的添加剂分解，而漂移可能具有独立感兴趣。
We show that the last zero before time $t$ of a recurrent Bessel process with drift starting at $0$ has the same distribution as the product of an independent right censored exponential random variable and a beta random variable. This extends a recent result of Schulte-Geers and Stadje (2017) from Brownian motion with drift to recurrent Bessel processes with drift. Our proof is intuitive and direct while avoiding heavy computations. For this we develop a novel additive decomposition for the square of a Bessel process with drift that may be of independent interest.
