Large deviation principle for reflected Poisson driven stochastic differential equations in epidemic models

Abstract

We establish a large deviation principle for a reflected Poisson driven stochastic differential equation. Our motivation is to study in a forthcoming paper the problem of exit of such a process from the basin of attraction of a locally stable equilibrium associated with its law of large numbers. Two examples are described in which we verify the assumptions that we make to establish the large deviation principle.

Keywords:

• Poisson process
• law of large numbers
• large deviation principle

AMS subject classification:

• 60F10
• 60H10
• 92C60