论文标题
关于弥漫的最后一段时间的分解
On Decomposition of the Last Passage Time of Diffusions
论文作者
论文摘要
对于常规的瞬态扩散，我们将其最后一次通过时间分解为某个状态$α$。这是通过使用高于$α$的领域的职业时间将原始扩散转换为两个扩散来实现的。基于这两个过程，两者都在$α$处具有反射边界，我们得出了最后一个段落时间的拉普拉斯变换的分解公式，以简单的形式以绿色功能为简单形式。该方程还导致绿色函数的分解公式。我们证明了这些公式在具有两个值参数的扩散中的应用。
For a regular transient diffusion, we provide a decomposition of its last passage time to a certain state $α$. This is accomplished by transforming the original diffusion into two diffusions using the occupation time of the area above and below $α$. Based on these two processes, both having a reflecting boundary at $α$, we derive the decomposition formula of the Laplace transform of the last passage time explicitly in a simple form in terms of Green functions. This equation also leads to the Green function's decomposition formula. We demonstrate an application of these formulas to a diffusion with two-valued parameters.
