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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 Contraction principle (large deviations theory) ： ウィキペディア英語版 Contraction principle (large deviations theory) In mathematics — specifically, in large deviations theory — the contraction principle is a theorem that states how a large deviation principle on one space "pushes forward" to a large deviation principle on another space ''via'' a continuous function. ==Statement of the theorem== Let ''X'' and ''Y'' be Hausdorff topological spaces 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 ''T'' : ''X'' → ''Y'' be a continuous function, and let ''ν''''ε'' = ''T''∗(''μ''''ε'') be the push-forward measure of ''μ''''ε'' by ''T'', i.e., for each measurable set/event ''E'' ⊆ ''Y'', ''ν''''ε''(''E'') = ''μ''''ε''(''T''−1(''E'')). Let :$J(y)\; :=\; \backslash inf\; \backslash big\backslash ,$ with the convention that the infimum of ''I'' over the empty set ∅ is +∞. Then: * ''J'' : ''Y'' → () is a rate function on ''Y'', * ''J'' is a good rate function on ''Y'' if ''I'' is a good rate function on ''X'', and * (''ν''''ε'')''ε''>0 satisfies the large deviation principle on ''Y'' with rate function ''J''. 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「Contraction principle (large deviations theory)」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.