Modified Runge-Kutta methods for pathwise approximations of SDEs
schedule le lundi 28 octobre 2019 de 17h00 à 18h00
Organisé par : F. Bechtold, W. Da Silva , A. Fermanian, S. Has, Y. Yu
Intervenant : F. Bechtold (LPSM)
Lieu : P6 Jussieu 16-26-209
Sujet : Modified Runge-Kutta methods for pathwise approximations of SDEs
Abstract: The convergence of numerical schemes such as the Euler-Maruyama method for stochastic differential equations is usually quantified in terms of strong or weak convergence which both involve averages over sample paths. This comes as no surprise, if one recalls that Itô calculus is a fundamentally non-pathwise theory. By using rough path theory (a pathwise stochastic calculus) instead of Itô calculus one is able to systematically investigate pathwise convergences of Runge-Kutta schemes and establish new ones by exploiting close analogies to the ODE theory. We will discuss Runge-Kutta methods in the ODE setting and an introduction to the theory of rough paths and show how these can be merged to come up with stochastic Runge-Kutta methods for SDEs and results on their pathwise convergence.