# Large deviations for neutral stochastic functional differential equations

## TL;DR

This paper investigates large deviations in neutral stochastic functional differential equations using an exponential approximation method under a one-sided Lipschitz condition.

## Contribution

It introduces a novel approach employing contraction principle and exponential approximation for large deviations analysis in this class of equations.

## Key findings

- Established large deviation principles for neutral stochastic functional differential equations.
- Extended the applicability of large deviations techniques to equations with neutral terms.
- Provided theoretical foundations for future probabilistic analysis of such equations.

## Abstract

In this paper, under a one-sided Lipschitz condition on the drift coefficient we adopt (via contraction principle) a exponential approximation argument to investigate large deviations for neutral stochastic functional differential equations.