ANALYSIS OF INVARIANT MEASURES AND LANGEVIN DYNAMICS IN STOCHASTIC DIFFERENTIAL SYSTEMS
We investigate diffusive processes characterized by drift within the ndimensional 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 nonreversible dynamics. Physical Langevintype processes, defined on the phase space of position and velocity, where stochastic perturbations influence the velocity component exclusively, are elegantly contextualized within this theoretical framework.
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