Exact simulation for the first hitting time of Brownian motion and Brownian bridge

被引：1

作者：

Taeho, Lee ^{[1
]}

机构：

[1] Korea Adv Inst Sci & Technol, Daejeon, South Korea

来源：

STATISTICS & PROBABILITY LETTERS | 2023年 / 193卷

关键词：

Brownian motion; Brownian bridge; First hitting time; Exact simulation; CROSSING PROBABILITIES;

D O I：

10.1016/j.spl.2022.109654

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 propose an exact simulation scheme for the first hitting time of Brownian motion. Our method is applicable to expanding boundaries, which are linear or piecewise linear. We first develop an algorithm for symmetric linear boundaries, and then extend it to other boundaries using a localization technique. The extended algorithm iteratively invokes a symmetric-case algorithm, and we prove that the expected number of iterations is uniformly bounded. We apply our scheme to simulate the first hitting time of a Brownian bridge.(c) 2022 Published by Elsevier B.V.

引用

页数：8

共 18 条

[1] Some conditional crossing results of Brownian motion over a piecewise-linear boundary [J].