In mathematics, the Dawson–GĂ€rtner theorem is a result in large deviations theory. Heuristically speaking, the Dawson–GĂ€rtner theorem allows one to transport a large deviation principle on a âsmallerâ topological space to a âlargerâ one.
Let (Yj)jâJ be a projective system of Hausdorff topological spaces with maps pij : Yj â Yi. Let X be the projective limit (also known as the inverse limit) of the system (Yj, pij)i,jâJ, i.e.
Let (με)ε>0 be a family of probability measures on X. Assume that, for each j â J, the push-forward measures (pjâμε)ε>0 on Yj satisfy the large deviation principle with good rate function Ij : Yj â R âȘ {+â}. Then the family (με)ε>0 satisfies the large deviation principle on X with good rate function I : X â R âȘ {+â} given by
In mathematics, the Dawson–GĂ€rtner theorem is a result in large deviations theory. Heuristically speaking, the Dawson–GĂ€rtner theorem allows one to transport a large deviation principle on a âsmallerâ topological space to a âlargerâ one.
Let (Yj)jâJ be a projective system of Hausdorff topological spaces with maps pij : Yj â Yi. Let X be the projective limit (also known as the inverse limit) of the system (Yj, pij)i,jâJ, i.e.
Let (με)ε>0 be a family of probability measures on X. Assume that, for each j â J, the push-forward measures (pjâμε)ε>0 on Yj satisfy the large deviation principle with good rate function Ij : Yj â R âȘ {+â}. Then the family (με)ε>0 satisfies the large deviation principle on X with good rate function I : X â R âȘ {+â} given by