By using the law of the excursions of Brownian motion with drift, we find thedistribution of the $n-$th passage time of Brownian motion through a straightline $S(t)= a + bt.$ In the special case when $b = 0,$ we extend the result toa space-time transformation of Brownian motion.
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机译:通过使用布朗运动随漂移的偏移定律,我们发现布朗运动的第n次通过时间通过直线$ S(t)= a + bt的分布。在特殊情况下,当$ b = 0,$我们将结果扩展为布朗运动的时空变换。
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