The local linearization scheme for nonlinear diffusion models with discontinuous coefficients

The local linearization scheme, defined in Shoji and Ozaki [1997, J. Time Ser. Anal. 18, 485-506] for diffusions with smooth coefficients, is studied under some regularity conditions when the coefficients are not necessarily continuous. It is shown that the local scheme converges weakly to the diffusion itself. These results are applied to continuous-time threshold autoregressive moving-average processes and multi-dimensional continuous-time threshold AR models.