Abstract

Let X(t) be a time-homogeneous jump-diffusion process. We assume that the jump size depends on the value of X(t). We obtain analytical results for the moments of T(x) and of $X(T(x)),$ where T(x) is the first time that the process leaves the interval (a, b). We also compute $P[X(T(x))\le a].$ These results have applications in financial mathematics.

中文翻译：

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具有状态相关跳跃的扩散过程的首过问题

摘要

令X ( t ) 是一个时间齐次的跳跃扩散过程。我们假设跳跃大小取决于X ( t ) 的值。我们得到T ( x ) 和$X(吨(X)),$其中T ( x ) 是过程第一次离开区间 ( a , b )。我们还计算$磷[X(吨(X))\le \mathrm{一种}].$这些结果在金融数学中有应用。