Pathwise methods for a class of SDEs with non-globally Lipschitz coefficients
Hugo de la Cruz (School of Applied Mathematics. FGV EMAp), Mario Munoz
We propose an approach for the numerical integration of a class of multiplicative-noise SDEs with non-globally Lipschitz coefficients. For this, me devise an appropriate invertible continuous transformation, that allows to conjugate the flow of the SDE to the flow of a non-autonomous random differential equation which has the stationary Ornstein-Uhlenbeck process as the only input parameter of the system. In this way, based on this explicit conjugacy between both equations, new discrete-time approximations are constructed. Convergence results are presented, and some simulation studies are carried out to illustrate the practical performance of the introduced approach.