Desmond J. Higham, Xuerong Mao, Andrew M. Stuart, Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations, SIAM Journal on Numerical Analysis, Vol. 40, No. 3 (2003), ...

Our analysis is motivated by an example of an exponentially almost surely stable nonlinear SDE for which the Euler-Maruyama (EM) method fails to reproduce this behavior for any nonzero timestep. We ...