Mery, Christophe-Aschkan2014-02-042014-02-042014-02-042013https://infoscience.epfl.ch/handle/20.500.14299/100381This project offers a rigorous introduction to the tools needed to construct a continuous stochastic process. Among other things, we give a very detailed proof of the Kolmogorov continuity criterion. We then construct a Brownian Motion following the formalism of D. Revuz and M. Yor. That is, we see the BM as a linear isometry from a Hilbert space into a Gaussian space.Brownian MotionStochastic Processtext::working paper