2025/07/28 by Eric Ávila-Vales, Ávila-Vales, Eric José, José Villa‐Morales +1
Decision Sciences · Economics, Econometrics and Finance · Physics and Astronomy · #35B09 #60G53 #65M06 #92B05 #FOS: Mathematics #Probabilistic and Robust Engineering Design #Probability (math.PR) #Stochastic processes and financial applications #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2508.02700
openalex publication_date 2025/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the distribution of exit times of the stochastic process within a bounded domain. These quantities are obtained by solving elliptic and parabolic partial differential equations (PDEs), respectively. To support practical applications, we propose a numerical scheme implemented in FreeFEM, emphasizing its effectiveness in two- and three-dimensional cases due to the software's limitations in higher dimensions. The examples provided illustrate the theoretical results, which extend known one-dimensional solutions to higher-dimensional settings. This contribution bridges theoretical and computational approaches for analyzing stochastic processes in multidimensional domains, offering insights into their behavior and potential applications.