New Methods for Calculating First Passage Times in Drifted Diffusion Processes

Recent research by Juan Magalang and colleagues presents two innovative methods for calculating the distribution of first passage times in drifted diffusion processes with stochastic resetting and mixed boundary conditions. The study introduces a 'Padé-partial fraction' approximation, which utilizes the Padé approximation to the Laplace transform of the first passage time distribution, allowing for exact inversion through partial fraction decomposition. Additionally, a 'multiresolution algorithm' is proposed, employing a Monte Carlo technique that leverages the properties of the Wiener process to generate Brownian bridges at varying resolutions.

The findings indicate that the multiresolution algorithm demonstrates higher efficiency compared to standard Monte Carlo methods. Meanwhile, the Padé-partial fraction method is noted for its accuracy across different scenarios and provides an analytical formula for expected first passage times. This research contributes to the understanding of diffusion processes, which have applications in various fields, including physics, biology, and finance, where the timing of events is crucial.

The full paper can be accessed at arXiv:2311.03939.