Change of Measure Enhanced Near-Exact Euler–Maruyama Scheme for the Solution to Nonlinear Stochastic Dynamical Systems

Abstract

The present study utilizes the Girsanov transformation-based framework for solving a nonlinear stochastic dynamical system in an efficient way in comparison with other available approximate methods. In this approach, rejection sampling is formulated to evaluate the Radon–Nikodym derivative arising from the change of measure due to Girsanov transformation. Rejection sampling is applied on the Euler–Maruyama approximated sample paths, which draw exact paths independent of the diffusion dynamics of the underlying dynamical system. The efficacy of the proposed framework was ensured using more accurate numerical as well as exact nonlinear methods. Finally, nonlinear applied test problems were considered to confirm the theoretical results. The test problems demonstrated that the proposed exact formulation of the Euler–Maruyama provides an almost exact approximation to both the displacement and velocity states of a second-order nonlinear dynamical system.