Likelihood ratios for signals in additive white noise

We present a formula for likelihood functionals for signals in which the corrupting noise is modelled as white noise rather than the usual Wiener process. The main difference is the appearance of an additional term corresponding to the conditional mean square error. By way of one application we consider the order-disorder problem of Shiryayev.Research supported in part under Grant No. 73-2492, Applied Math. Divn., AFOSR, USAF.