Stokes formula on the Wiener space and n-dimensional Nourdin–Peccati analysis

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• 作者：Hé ; lè ; ne Airault ; Paul Malliavin ; Frederi Viens
• 关键词：Wiener space ; Quasi-sure analysis ; Density formula ; Nourdin– ; Peccati analysis ; Stein's lemma ; Conditional probability
• 刊名：Journal of Functional Analysis
• 出版年：2010
• 出版时间：1 March 2010
• 年：2010
• 卷：258
• 期：5
• 页码：1763-1783
• 全文大小：210 K

文摘

Extensions of the Nourdin–Peccati analysis to Rⁿ-valued random variables are obtained by taking conditional expectation on the Wiener space. Several proof techniques are explored, from infinitesimal geometry, to quasi-sure analysis (including a connection to Stein's lemma), to classical analysis on Wiener space. Partial differential equations for the density of an Rⁿ-valued centered random variable Z=(Z¹,…,Zⁿ) are obtained. Of particular importance is the function defined by the conditional expectation given Z of the auxiliary random matrix , i,j=1,2,…,n, where D and are respectively the derivative operator and the generator of the Ornstein–Uhlenbeck semigroup on Wiener space.