Moderate Deviation Principle for dynamical systems with small random perturbation

Yutao ma, Ran Wang, Liming Wu

Consider the stochastic differential equation in $\rr^d$ dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}σ(X^\e_t)dB_t X^{\e}_0&=x_0,\quad x_0\in\rr^d$where$b:\rr^d\to\rr^d$is$C^1$ such tha…