Moderate deviation and central limit theorem for SDDEs with plynomial growth

TL;DR

This paper studies the moderate deviation principle and central limit theorem for stochastic delay differential equations with polynomial growth coefficients, using weak convergence methods and variational representations.

Contribution

It introduces new results on moderate deviations and CLT for SDDEs with nonlinear growth, extending existing theories to more complex coefficient behaviors.

Findings

Established moderate deviation principles for SDDEs with small noise.

Proved CLT for SDDEs with polynomial growth in delay variables.

Extended theoretical understanding of stochastic delay equations with nonlinear coefficients.

Abstract

In this paper, employing the weak convergence method, based on a variational representation for expected values of positive functionals of a Brownian motion, we investigate moderate deviation %(CLT for abbreviation) for a class of stochastic differential delay equations with small noises, where the coefficients 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 coefficients are polynomial growth with respect to the delay variables.