On the Joint Distribution of First-passage Time and First-passage Area of Drifted Brownian Motion

被引：0
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作者：
Mario Abundo
Danilo Del Vescovo
机构：
[1] Università “Tor Vergata”,Dipartimento di Matematica
[2] via della Ricerca Scientifica,undefined
来源：
Methodology and Computing in Applied Probability | 2017年 / 19卷
关键词：
First-passage time; First-passage area; One-dimensional diffusion; 60J60; 60H05; 60H10;
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摘要：
For drifted Brownian motion X(t) = x-µt + Bt (µ > 0) starting from x > 0, we study the joint distribution of the first-passage time below zero ,t(x), and the first-passage area ,A(x), swept out by X till the time t(x). In particular, we establish differential equations with boundary conditions for the joint moments E[t(x)mA(x)n], and we present an algorithm to find recursively them, for any m and n. Finally, the expected value of the time average of X till the time t(x) is obtained.
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页码：985 / 996
页数：11
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