Numerically Stable Simulation of Stochastic Differential Equations Driven by Empirical Processes

Project level: PhD, Masters

Stochastic differential equations driven by Brownian motion or L\'evy processes are well established as models for many real-world phenomena.  Just as there are efficient techniques for numerical integration of deterministic systems of differential equations (e.g. Runge--Kutta methods), there are well established counterparts for systems of stochastic differential equations driven by Brownian motion (see, for example, the book of Kloeden and Platen on the subject).   This project focuses on developing efficient and numerically-stable techniques for solving systems of stochastic differential equations driven by empirical processes (which could be related to a concurrent Monte Carlo simulation which may depend on the solution of the system of differential equations, for example).