Analytic semimartingales and their boundary values

A very general result for checking the existence of the C^∞-flows associated to the semimartingale-valued random fields is given in the first part of this paper. The following section contains the proof of the fact that any distribution-valued S¹-semimartingale can be represented as the boundary value of a semimartingale with values in the nuclear Fréchet space of the functions which are analytic outside the real line. In the last section, by the use of the Itô-Tanaka formula, the probabilistic solutions of a Schrödinger-type equation with reflection for any distribution as the initial condition is constructed.