Stochastic analysis without probability: study of some basic tools (Q619636)

In this article, authors propose a semi-group interpretation of essential notions and problems of stochastic analysis. By working on not necessarily Markovian semi-groups that arise from a big order generator, they define a generalized form of the Ito's formula with respect to this generator. They also define the Wiener distribution with respect to a convolution semi-group and they prove that this generalized distribution is the solution to the martingale problem associated to the generator mentioned before.