This thesis presents two independent research topics. Both are related to the application of stochastic problems to molecular dynamics. In the first part, we present a work related to the probabilistic interpretation of the Poisson-Boltzmann equation. This equation describes the electrostatic potential of a molecular system. After an introduction to the Poisson-Boltzmann equation, we focus on the parabolic and linear equation. After extending an existence and uniqueness result for backward stochastic differential equations, we establish a probabilistic interpretation of the nonlinear Poisson-Boltzmann equation with backward stochastic differential equations. Finally, in a more prospective second part, we initiate a study of a slow and fast variables detection method due to Paul Malliavin.
