Régularisation de l'équation de Langevin en dimension 1 par le mouvement Brownien fractionnaire
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The main goal of this paper is to provide a fractional stochastic differential equation modelling the physical phenomena governed by the Langevin equation in 1-dimension. A generalized equation leaning on the fractional Brownian motion (fBm) will be proposed, the later will allow a description of the complexity of the physical systems which escape any prediction of the of the standard Langevin equation. We shall begin at first to remind the basic notions of the standard Brownian motion (Bm) and the fractional Brownian motion (fBm), then, we shall establish a generalization to long memory of the Langevin equation.