A class of stochastic processes with a law generalizing a nondecomposable law on the real line

In this paper we define a class of stochastic processes where law can be considered as a natural generalization of a nondecomposable law. In particular case, we express the processes thus defined as semimartingales with a Brownian martingale part, and compute the likelihood for detecting a signal immersed in additive noise which looks like Brownian motion, but has different independence properties.