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Limit theorems on large deviations for semimartingales

Robert Sh. Liptser·Anatolii A. Pukhalskii
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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 Itô 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.

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Robert Sh. Liptser, Anatolii A. Pukhalskii. 2005-10-03. Limit theorems on large deviations for semimartingales. https://arxiv.org/abs/math/0510028

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