Approximation of ITO integrals arising in stochastic time-delayed systems

Likelihood functionals for stochastic linear time-delayed systems involve It?? integrals with respect to the observed data. Since Wiener process appearing in the standard observation process model for such systems is not realizable, and the physically realized process is smooth, one needs to study an approximation of such integrals by means of a smooth process; e.g., a band-limited process with no frequency component outside a finite, although large, band.