2020/06/08 by Mädälina Deaconu, Deaconu, Madalina, Samuel Herrmann +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematical Approximation and Integration #Nonlinear Partial Differential Equations #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2006.04378
openalex publication_date 2020/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper develops a new technique for the path approximation of one-dimensional stochastic processes, more precisely the Brownian motion and families of stochastic differential equations sharply linked to the Brownian motion (usually known as L and G-classes). We are interested here in the ε-strong approximation. We propose an explicit and easy to implement procedure that constructs jointly, the sequences of exit times and corresponding exit positions of some well chosen domains. The main results control the number of steps to cover a fixed time interval and the convergence theorems for our scheme. We combine results on Brownian exit times from time-depending domains (one-dimensional heat balls) and classical renewal theory. Numerical examples and issues are also described in order to complete the theoretical results.