Cumulants on the Wiener space

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• 作者：Ivan Nourdin ; Giovanni Peccati
• 关键词：Cumulants ; Diagram formulae ; Gaussian processes ; Malliavin calculus ; Ornstein– ; Uhlenbeck semigroup
• 刊名：Journal of Functional Analysis
• 出版年：2010
• 出版时间：1 June 2010
• 年：2010
• 卷：258
• 期：11
• 页码：3775-3791
• 全文大小：205 K

文摘

We combine infinite-dimensional integration by parts procedures with a recursive relation on moments (reminiscent of a formula by Barbour (1986)), and deduce explicit expressions for cumulants of functionals of a general Gaussian field. These findings yield a compact formula for cumulants on a fixed Wiener chaos, virtually replacing the usual “graph/diagram computations” adopted in most of the probabilistic literature.