Moderate deviations and Strassen's law for additive processes

Franziska Kühn, René L. Schilling

Published 2014-06-27, updated 2014-10-13Version 2

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 L\'evy process satisfies Strassen's law.