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Journal of Theoretical Probability

, Volume 29, Issue 2, pp 632–652 | Cite as

Moderate Deviations and Strassen’s Law for Additive Processes

  • Franziska KühnEmail author
  • René L. Schilling
Article

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 of Strassen’s functional law of the iterated logarithm. In particular, we show that any square-integrable Lévy process satisfies Strassen’s law.

Keywords

Moderate deviations Additive processes Strassen’s law Functional limit theorem 

Mathematics Subject Classification (2010)

Primary: 60F10 Secondary: 60F17 60G51 60G17 

Notes

Acknowledgments

Financial support through the Deutsche Forschungsgemeinschaft, DFG, Grant SCHI 419/5-2 is gratefully acknowledged.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institut für Mathematische Stochastik, Fachrichtung MathematikTechnische Universität DresdenDresdenGermany

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