期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2013
卷号：X
期号：2
页码：681-692
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：A well-known problem in Malliavin calculus concerns the relation betweenthe determinant of the Malliavin matrix of a random vector and the determinantof its covariance matrix. We give an explicit relation between these twodeterminants for couples of random vectors of multiple integrals. In particular, ifthe multiple integrals are of the same order and this order is at most 4, we provethat two random variables in the same Wiener chaos either admit a joint density, eitherare proportional and that the result is not true for random variables in Wienerchaoses of di erent orders.
关键词：multiple stochastic integrals; Wiener chaos; Malliavin matrix; covari-;ance matrix; existence of density.
