2024/12/17 by Devika Khurana, Sascha Desmettre, Khurana, Devika +3 · 2 citations
Computer Science · Engineering · Neuroscience · #37M05 #60G05 #60H35 #65C30 #68Q87 #92C20 #FOS: Mathematics #Molecular Junctions and Nanostructures #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Numerical Analysis (math.NA) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2412.13060
openalex publication_date 2024/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The first-passage time (FPT) is a fundamental concept in stochastic processes, representing the time it takes for a process to reach a specified threshold for the first time. Often, considering a time-dependent threshold is essential for accurately modeling stochastic processes, as it provides a more accurate and adaptable framework. In this paper, we extend an existing Exact simulation method developed for constant thresholds to handle time-dependent thresholds. Our proposed approach utilizes the FPT of Brownian motion and accepts it for the FPT of a given process with some probability, which is determined using Girsanov's transformation. This method eliminates the need to simulate entire paths over specific time intervals, avoids time-discretization errors, and directly simulates the first-passage time. We present results demonstrating the method's effectiveness, including the extension to time-dependent thresholds, an analysis of its time complexity, comparisons with existing methods through numerical examples, and its application to predicting spike times in a neuron.