Expansions for Repeated Integrals of Products with Applications to the Multivariate Normal
Christopher S. Withers, Saralees Nadarajah (2012)
ESAIM: Probability and Statistics
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We extend Leibniz' rule for repeated derivatives of a product to multivariate integrals of a product. As an application we obtain expansions for ( < < ) for ~ (0,) and for repeated integrals of the density of . When > 0 in the expansion for ( < ) reduces to one given by [H. Ruben B (1964) 3–11]. in terms of the moments of (0, ). This is shown to be a special case of an expansion in terms...