Mini-course on Stochastic Differential Equations
May 02-11, 2018 Jaume I University

The recent years has seen a growing interest in stochastic modeling as stochastic differential equations (SDEs) started to play a more and more important role in divers branches of science and industry. This includes, for instance, applications areas from biology (population growth models), mechanics (Langevin equation), or finance (Cox-Ingersoll-Ross model). Furthermore, as exact solutions to SDEs (basically an ordinary differential equation with the right hand side perturbed by a white noise) are rarely known, one must simulate SDEs numerically. It is therefore essential to understand basic concepts of convergence of numerical methods for SDEs. The mini-course will provide an accessible introduction to stochastic differential equations and numerical methods to solve them. The focus will be on main ideas and important concepts not on proving results. Furthermore, we will discuss applications from physics, biology, and finance. Prerequisites will be kept to a minimum (basic competence in algebra and calculus is assumed, familiarity with fundamental concepts from probability theory and numerical analysis helps).

Topics covered in this mini-course are: