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.

中文翻译：

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多维情况强势极限下的随机牛顿方程

我们考虑一类具有单井势函数的多维随机牛顿方程，并研究当势系数发散至无穷大时其求解过程的极限行为。通过引入几个新的随机过程，还给出了限制过程的显式公式。特别是，与一维情况不同，限制过程不是确定性的。