Moderate deviations and Strassen's law for additive processes

preprint2014arXivOpen access

Abstract

We establish a moderate deviation principle for processes with independent increments under certain growth conditions for the characteristics of the process. Using this moderate deviation principle, we give a new proof for Strassen's functional law of the iterated logarithm. In particular, we show that any square-integrable Lévy process satisfies Strassen's law.

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