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Large deviation principle for an estimator of the diffusion coefficient in a jump-diffusion process

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Abstract

We consider a jump-diffusion Lévy model, which is often used in financial and risk theory applications. Using discrete observations of the process, we consider a threshold estimator of the diffusion coefficient, and we show that it satisfies a large deviation principle. That gives us both the strong consistency of the estimator and an accurate measure of the estimation error.

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