Speaker. Hugo de la Cruz, FGV-School of Applied Mathematics, Brazil

Title. Exploring Adaptive Methods for Solving Stochastic Differential Equations

Abstract. Stochastic Differential Equations (SDEs) have become essential tools for modeling phenomena in diverse fields where noise plays a crucial role. In this talk, we will discuss how adaptive time-step integrators can be designed to reliably simulate the trajectories of the solutions to these equations. To make the presentation as self-contained as possible, we will first briefly introduce the theory of SDEs and their applications. Additionally, we will review important aspects of approximation methods for solving these equations, as well as some of the main challenges and pitfalls that often arise in the numerical simulation of stochastic systems. After this introductory part, we will present recent results concerning the construction and qualitative behavior of new adaptive exponential-type methods for SDEs. Simulation studies, including a comparative analysis with other integrators commonly used in applications, will be presented to confirm the practical advantages of the proposed adaptive methods.