Locking the Wiener Process to its Level-Crossing Time

被引：0

作者：

Schwarz, Wolf ^{[1
]}

Miller, Jeff O. ^{[2
]}

机构：

[1] Univ Potsdam, Fak Humanwissensch, D-14415 Potsdam, Germany

[2] Univ Dunedin, Dept Psychol, Dunedin, New Zealand

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2010年 / 39卷 / 02期

关键词：

First hitting model; Inverse Gaussian distribution; Response-locked time series; Wiener diffusion process; MODELING EVENT TIMES;

D O I：

10.1080/03610920902755821

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：

We consider the specific transformation of a Wiener process {X(t), t >= 0} in the presence of an absorbing barrier a that results when this process is "time-locked" with respect to its first passage time T(a) through a criterion level a, and the evolution of X(t) is considered backwards ( retrospectively) from T(a). Formally, we study the random variables defined by Y(t) = X(T(a) - t) and derive explicit results for their density and mean, and also for their asymptotic forms. We discuss how our results can aid interpretations of time series "response-locked" to their times of crossing a criterion level.

引用

页码：372 / 381

页数：10

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