On generalized inputs and white noise

A brief sketch is given of recent work by this author and by M. Fliess on generalized inputs. The aim is to develop a theory in which stochastic differential equations driven by white noise can be solved for each sample path. The results obtained so far are complete for the case of equations driven by a scalar white noise, as well as for bilinear systems driven by vector-valued inputs. The main idea is to regard the "sample paths of a white noise process" as "generalized functions" in a sense different from the theory of distributions. A representation of these generalized functions as formal power series is discussed.