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 ${\int }_0^t{\sup }_{x\in {\mathbb{R}}^d}||\sigma (s,x)||\vee |b(s,x)|ds=:C_t<\infty$ for any fixed $t$, then we generalize the conclusion to unbounded case by using bounded approximation program.

13 pages

References in corpus (1)

• New sufficient conditions of existence, moment estimations and non confluence for SDEs with non-Lipschitzian coefficients