Dynamic Euler Discretization of Exploding Processes

Abstract

We propose a new numerical method to accurately simulate the trajectory of stochastic differential equations with exploding coefficients. The approach relies on the Euler method, where we dynamically choose the step size to obtain the desired root-mean-square error. To determine the step size, we rely on the toy model of the explosion model in which an analytical solution is available. We demonstrated the superiority of the dynamic Euler approach compared to the fixed step size method (standard Euler method) based on simulation experiments.