Exponential Approximations in Completely Regular Topological Spaces and Extensions of Sanov's Theorem

Peter Eichelsbacher and Uwe Schmock

Abstract: This paper is devoted to the well known transformations that preserve a large deviation principle (LDP), namely, the contraction principle with approximately continuous maps and the concepts of exponential equivalence and exponential approximations. We generalize these transformations to completely regular topological state spaces, give some examples and, as an illustration, reprove a generalization of Sanov's theorem, due to de Acosta. Using partition-dependent couplings, we then extend this version of Sanov's theorem to triangular arrays and prove a full LDP for the empirical measures of exchangeable sequences with a general measurable state space.

Keywords: large deviations, exponential equivalence, contraction principle, gauge space, uniform space, approximately continuous map, triangular array, exchangeable sequence

2010 Mathematics Subject Classification:

Reference: Stochastic Processes and Their Applications, Vol. 77 (1998), No. 2, 139-154

DOI: 10.1016/S0304-4149(98)00047-7

The paper (17 pages, revised version, May 26, 1998) is available in:

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