Abstract In this paper the joint distribution of the maximum increase and the maximum decrease up to a first hitting time is calculated for a regular one-dimensional diffusion. Moreover, it is shown that the process given by the maximum decrease when the hitting level is the “time” parameter is a pure jump Markov process and its generator is found. As examples, Brownian motion and three dimensional Bessel process are analyzed more in detail.

中文翻译：

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关于一维扩散的最大增减

摘要 本文计算了规则一维扩散到第一次击球时间的最大增加和最大减少的联合分布。此外，还表明当击球水平为“时间”参数时最大减少给出的过程是一个纯跳跃马尔可夫过程，并找到了它的生成器。作为例子，更详细地分析了布朗运动和三维贝塞尔过程。