Abstract

Under exponential tightness hypothesis, we show that the large deviation functional Λ ¯ ( · ) has the same variational form as when large deviations hold. As an application, we identify the affine regularization of a rate function on any real Hausdorff topological vector space in terms of Λ ¯ ( · ) . Some classical results involving the generalized log-moment generating function are improved.

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