Approximation of itô integrals arising in stochastic time-delayed systems

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