Moderate deviation and central limit theorem for stochastic differential delay equations with polynomial growth

Abstract

Employing the weak convergence method, based on a variational representation for expected values of positive functionals of a Brownian motion, we investigate moderate deviation for a class of stochastic differential delay equations with small noises, where the coeffcients are allowed to be highly nonlinear growth with respect to the variables. Moreover, we obtain the central limit theorem for stochastic differential delay equations which the coeffcients are polynomial growth with respect to the delay variables.

Key words： Stochastic differential delay equation (SDDE); polynomial growth; central limit theorem; moderate deviation principle; weak convergence

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