Large deviations for neutral functional SDEs with jumps

Abstract

In this paper, by the weak convergence method, based on a variational representation for positive functionals of a Poisson random measure and Brownian motion, we establish uniform large deviation principles (LDPs) for a class of neutral stochastic differential equations driven by jump processes. As a byproduct, we also obtain uniform LDPs for neutral stochastic differential delay equations which, in particular, allow the coefficients to be highly nonlinear with respect to the delay argument.

Keywords::

• neutral functional stochastic differential equation
• uniform large deviation principle
• highly nonlinear growth
• Poisson random measure

AMS Subject Classification::

• 60H10
• 60F10

Acknowledgement

We are indebted to the referee for his/her valuable comments which have greatly improved our earlier version.

Notes

^1. Email: [email protected]