A new approach to the problem of finding the distribution of integral functionals under the excursion measure is presented. It is based on the technique of excursion straddling a time, stochastic analysis, and calculus on local time, and it is done for Brownian motion with drift reflecting at 0, and under some additional assumptions for some class of Itó diffusions. The new method is an alternative to the classical potential-theoretic approach and gives new specific formulas for distributions under the excursion measure.

中文翻译：

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偏移量度下的积分泛函

提出了一种求解偏移测度下积分泛函分布问题的新方法。它基于跨越时间的偏移、随机分析和本地时间微积分的技术，它是针对漂移反射为 0 的布朗运动完成的，并且是在对某些类别的伊藤扩散的一些额外假设下完成的。新方法是经典势论方法的替代方法，并为偏移测量下的分布提供了新的特定公式。