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Moderate Deviations and Strassen’s Law for Additive Processes

Author

Listed:
  • Franziska Kühn

    (Technische Universität Dresden)

  • René L. Schilling

    (Technische Universität Dresden)

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.

Suggested Citation

  • Franziska Kühn & René L. Schilling, 2016. "Moderate Deviations and Strassen’s Law for Additive Processes," Journal of Theoretical Probability, Springer, vol. 29(2), pages 632-652, June.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:2:d:10.1007_s10959-014-0584-6
    DOI: 10.1007/s10959-014-0584-6
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    References listed on IDEAS

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    1. Puhalskii, A., 1994. "The method of stochastic exponentials for large deviations," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 45-70, November.
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