Moderate deviations and Strassen's law for additive processes
  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. 
Franziska K\"uhn and Ren\'e L. Schilling
math.PR