ANALYSIS OF INVARIANT MEASURES AND LANGEVIN DYNAMICS IN STOCHASTIC DIFFERENTIAL SYSTEMS
We investigate diffusive processes characterized by drift within the n dimensional Euclidean space R n , particularly focusing on stochastic differential equations. We summarize the interdependencies between the drift vector, the diffusion matrix, and invariant distributions, utilizing the appropriate variables . This approach reveals a decomposition into 'potential' and 'geometric' components, with the geometric part encapsulating non reversible dynamics. Physical Langevin type processes, defined on the phase space of position and velocity, where stochastic perturbations...