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Principles of Large Deviations for the Empirical Processes of the Ornstein–Uhlenbeck Process

Author

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  • Matthias K. Heck

    (Courant Institute of Mathematical Sciences)

Abstract

The present paper deals with principles of large deviations for the empirical processes of the Ornstein–Uhlenbeck process. One such principle due to Donsker and Varadhan is well known. It uses as underlying space C(ℝ, ℝ d ) endowed with the topology of uniform convergence on compact sets. The principles of large deviations proved in the present paper use as underlying spaces appropriate subspaces of C(ℝ, ℝ d ) endowed with weighted supremum norms. These principles are natural generalizations of the principle of Donsker and Varadhan.

Suggested Citation

  • Matthias K. Heck, 1999. "Principles of Large Deviations for the Empirical Processes of the Ornstein–Uhlenbeck Process," Journal of Theoretical Probability, Springer, vol. 12(1), pages 147-179, January.
    • Handle: RePEc:spr:jotpro:v:12:y:1999:i:1:d:10.1023_a:1021700811752
    DOI: 10.1023/A:1021700811752
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    Cited by:

    1. Alain Rouault & Marc Yor & Marguerite Zani, 2002. "A Large Deviations Principle Related to the Strong Arc-Sine Law," Journal of Theoretical Probability, Springer, vol. 15(3), pages 793-815, July.

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