Free-differentiability conditions on the free-energy function implying large deviations
نویسنده
چکیده
Let (μα) be a net of Radon sub-probability measures on R, and (tα) be a net in ]0,+∞[ converging to 0. Assuming that the generalized log-moment generating function L(λ) exists for all λ in a nonempty open interval G, we give conditions on the left or right derivatives of L|G, implying vague (and thus narrow when 0 ∈ G) large deviations. The rate function (which can be nonconvex) is obtained as an abstract Legendre-Fenchel transform. This allows us to strengthen the Gärtner-Ellis theorem by removing the usual differentiability assumption. A related question of R. S. Ellis is solved.
منابع مشابه
Differentiability-free conditions on the free-energy function implying large deviations
Let (μα) be a net of Radon sub-probability measures on R, and (tα) be a net in ]0, 1] converging to 0. Assuming that the generalized log-moment generating function L(λ) exists for all λ in a nonempty open intervalG, we give conditions on the left or right derivatives of L|G, implying a vague (and thus narrow when 0 ∈ G) large deviation principle. The rate function (which can be nonconvex) is ob...
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