On the First-Passage Area of a One-Dimensional Jump-Diffusion Process

被引：12

作者：

Abundo, Mario ^{[1
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

来源：

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2013年 / 15卷 / 01期

关键词：

First-passage time; First-passage area; One-dimensional jump-diffusion; BROWNIAN-MOTION;

D O I：

10.1007/s11009-011-9223-1

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

For a one-dimensional jump-diffusion process X(t), starting from x > 0, it is studied the probability distribution of the area A(x) swept out by X(t) till its first-passage time below zero. In particular, it is shown that the Laplace transform and the moments of A(x) are solutions to certain partial differential-difference equations with outer conditions. The distribution of the maximum displacement of X(t) is also studied. Finally, some explicit examples are reported, regarding diffusions with and without jumps.

引用

页码：85 / 103

页数：19

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