Stochastic Newton equations in the strong potential limit for the multi-dimensional case

Abstract

We consider a type of stochastic Newton equations in multi-dimension, with single-well potential functions, and study the limiting behaviors of their solution processes when the coefficients of the potentials diverge to infinity. The explicit formulations of the limiting processes are also given, by introducing several new stochastic processes. Especially, different from the one-dimensional case, the limiting processes are not deterministic.