Exponential decay of correlation for the Stochastic Process associated to the Entropy Penalized Method

In this paper we present an upper bound for the decay of correlation for the stationary stochastic process associated with the Entropy Penalized Method. Let L(x, v) : T × R → R be a C Lagrangian of the form L(x, v) = 1 2 |v| 2 − U(x) + 〈P, v〉. We point out that we do not assume more differentiability of L according the the dimension of the torus T. 1. Definitions and the set up of the problem Let T be the n-dimensional torus. In this paper we assume that the Lagrangian, L(x, v) : T × R → R has the form L(x, v) = 1 2 |v| − U(x) + 〈P, v〉, where U ∈ C(T), and P ∈ R is constant. 1 Partially supported by the Center for Mathematical Analysis, Geometry and Dynamical Systems through FCT Program POCTI/FEDER and also by grant POCI/FEDER/MAT/55745/2004. 2 Partially, supported by CNPq, PRONEX – Sistemas Dinâmicos, Instituto do Milênio, and beneficiary of CAPES financial support.