  The present study utilizes the Girsanov transformation based framework for
solving a nonlinear stochastic dynamical system in an efficient way in
comparison to other available approximate methods. In this approach, a
rejection sampling is formulated to evaluate the Radon-Nikodym derivative
arising from the change of measure due to Girsanov transformation. The
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 is ensured using more
accurate numerical as well as exact nonlinear methods. Finally, nonlinear
applied test problems are considered to confirm the theoretical results. The
test problems demonstrates 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 non-linear dynamical system.
