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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Tilted large deviation principle ： ウィキペディア英語版 Tilted large deviation principle In mathematics — specifically, in large deviations theory — the tilted large deviation principle is a result that allows one to generate a new large deviation principle from an old one by "tilting", i.e. integration against an exponential functional. It can be seen as an alternative formulation of Varadhan's lemma. ==Statement of the theorem== Let ''X'' be a Polish space (i.e., a separable, completely metrizable topological space), and let (''μ''''ε'')''ε''>0 be a family of probability measures on ''X'' that satisfies the large deviation principle with rate function ''I'' : ''X'' → (). Let ''F'' : ''X'' → R be a continuous function that is bounded from above. For each Borel set ''S'' ⊆ ''X'', let :$J\_\; (S)\; =\; \backslash int\_\; e^\; \backslash ,\; \backslash mathrm\; \backslash mu\_\; (x)$ and define a new family of probability measures (''ν''''ε'')''ε''>0 on ''X'' by :$\backslash nu\_\; (S)\; =\; \backslash frac.$ Then (''ν''''ε'')''ε''>0 satisfies the large deviation principle on ''X'' with rate function ''I''''F'' : ''X'' → () given by :$I^\; (x)\; =\; \backslash sup\_\; \backslash big(F(y)\; -\; I(y)\; \backslash big)\; -\; \backslash big(F(x)\; -\; I(x)\; \backslash big).$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Tilted large deviation principle」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.