|
In mathematics, Varadhan's lemma is a result from large deviations theory named after S. R. Srinivasa Varadhan. The result gives information on the asymptotic distribution of a statistic ''φ''(''Z''''ε'') of a family of random variables ''Z''''ε'' as ''ε'' becomes small in terms of a rate function for the variables. ==Statement of the lemma== Let ''X'' be a regular topological space; let (''Z''''ε'')''ε''>0 be a family of random variables taking values in ''X''; let ''μ''''ε'' be the law (probability measure) of ''Z''''ε''. Suppose that (''μ''''ε'')''ε''>0 satisfies the large deviation principle with good rate function ''I'' : ''X'' → (). Let ''ϕ'' : ''X'' → R be any continuous function. Suppose that at least one of the following two conditions holds true: either the tail condition : where 1(''E'') denotes the indicator function of the event ''E''; or, for some ''γ'' > 1, the moment condition : Then : 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「Varadhan's lemma」の詳細全文を読む スポンサード リンク
|