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, ℝd) 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, ℝd) endowed with weighted supremum norms. These principles are natural generalizations of the principle of Donsker and Varadhan.
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Heck, M.K. Principles of Large Deviations for the Empirical Processes of the Ornstein–Uhlenbeck Process. Journal of Theoretical Probability 12, 147–179 (1999). https://doi.org/10.1023/A:1021700811752
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DOI: https://doi.org/10.1023/A:1021700811752