Large deviation principle of SDEs with non-Lipschitzian coefficients under localized conditions

Abstract: Localized sufficient conditions for the large deviation principle of the given stochastic differential equations will be presented for stochastic differential equations with non-Lipschitzian and time-inhomogeneous coefficients, which is weaker than those relevant conditions existing in the literature. We consider at first the large deviation principle when $\int_0<sup>t\sup_{x\in\mathbb{R}<sup>d}||\sigma(s,x)||\vee|b(s,x)|ds=:C_t&lt;\infty$ for any fixed $t$, then we generalize the conclusion to unbounded case by using bounded approximation program.