Limit theorems on large deviations for semimartingales

Abstract

We consider a sequence $X^n=(X^n_t)_{t\ge 0},n\ge 1$ of semimartingales. Each $X^n$ is a weak solution to an It\^o equation with respect to a Wiener process and a Poissonian martingale measure and is in general non-Markovian process. For this sequence, we prove the large deviation principle in the Skorokhod space $D=D_{[0,\infty)}$. We use a new approach based on of exponential tightness. This allows us to establish the large deviation principle under weaker assumptions than before.