The numerical solution of random ODEs

Abstract

Random ODEs are ordinary differential equations that include a stochastic process in their vector field. They can be analysed pathwise using deterministic calculus. Since the sample paths of the driving stochastic process is at most Hölder continuous, they lack the smoothness in their time variable to justify the convergence analysis of classical numerical scheme for ODEs. It will be briefly indicated here how new classes of numerical schemes can be derived to ensure high order of pathwise convergence depending on the nature of the driving stochastic processes.