WEAK CONSISTENCY OF THE EULER METHOD FOR NUMERICALLY SOLVING STOCHASTIC DIFFERENTIAL-EQUATIONS WITH DISCONTINUOUS COEFFICIENTS

We prove that, under appropriate conditions, the sequence of approxima te solutions constructed according to the Euler scheme converges weakl y to the (unique) solution of a stochastic differential equation with discontinuous coefficients. We also obtain a sufficient condition for the existence of a solution to a stochastic differential equation with discontinuous coefficients. These results are then applied to justify the technique of simulating continuous-time threshold autoregressive moving-average processes via the Euler scheme. (C) 1998 Elsevier Scien ce B.V. All rights reserved.