Computation of the Survival Probability of Brownian Motion with Drift Subject to an Intermittent Step Barrier

This article provides an exact formula for the survival probability of Brownian motion with drift when the absorbing boundary is defined as an intermittent step barrier, i.e., an alternate sequence of time intervals when the boundary is piecewise constant, and time intervals without any defined boun...

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Bibliographic Details
Published in:AppliedMath Vol. 4; no. 3; pp. 1080 - 1097
Main Author: Guillaume, Tristan
Format: Journal Article
Language:English
Published: MDPI AG 01.09.2024
Subjects:
boundary crossing
Brownian motion
first-passage time
intermittent barrier
step barrier
survival probability
ISSN:2673-9909, 2673-9909
Online Access:Get full text
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Summary:This article provides an exact formula for the survival probability of Brownian motion with drift when the absorbing boundary is defined as an intermittent step barrier, i.e., an alternate sequence of time intervals when the boundary is piecewise constant, and time intervals without any defined boundary. Numerical implementation is dealt with by a simple and robust Monte Carlo integration algorithm directly derived from the formula, which compares favorably with conditional Monte Carlo simulation. Exact analytical benchmarks are also provided to assess the accuracy of the numerical implementation.
ISSN:2673-9909
2673-9909
DOI:10.3390/appliedmath4030058