Evaluation of Likelihood Functionsi"

An expression is obtained for the likelihood function for the detec-tion of a stochastic signal (diffusion process) in white noise. A sto-chastic differential equation is then obtained for the evolution of the likelihood function and the coefficients of this differential equation are related to a corresponding nonlinear filtering problem. Some ex-tensions are noted to diffusion process ignals in correlated noise and to more general stochastic signals. 1