Stochastic analysis without probability: study of some basic tools. (English) Zbl 1233.47036

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.


47D07 Markov semigroups and applications to diffusion processes
47D08 Schrödinger and Feynman-Kac semigroups
60G07 General theory of stochastic processes
60G20 Generalized stochastic processes
60G48 Generalizations of martingales
60H40 White noise theory
60J60 Diffusion processes
60J65 Brownian motion
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