Some conditional and unconditional expectation identities for the multivariate normal with non-zero mean

Authors : Christopher S WİTHERS, Saralees NADARAJAH

Pages : 679-687

View : 20 | Download : 9

Publication Date : 2014-08-01

Article Type : Research Paper

Abstract :We give formulas for the conditional and unconditional expectations of products of multivariate Hermite and modified Hermite polynomials, each with a multivariate normal argument. A unified approach is given that covers both of these polynomials, each associated with a covariance matrix. This extended Hermite polynomial is associated with a matrix which is the difference between two covariance matrices, in other words, with any symmetric matrix. 
Keywords : Conditional expectation, Multivariate Hermite polynomial, Multivariate normal