P. Szabłowski

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math.PR2026

The conditional expectation of the product of the first $n - 1$ Hermite polynomials in a multivariate normal distribution with respect to the $n$ -th variable. A fresh perspective on the Kibble-Slepian formula

PaweÅ J. SzabÅowski

We calculate the conditional expectation of $\prod_{j = 1}^{n - 1} H_{k_{j}}$ given $X_{n} = z,$ if random vector $(X_{1}, \dots, X_{n})^{T}$ has multivariate normal distribution…

The conditional expectation of the product of the first n−1 Hermite polynomials in a multivariate normal distribution with respect to the n-th variable. A fresh perspective on the Kibble-Slepian formula

The conditional expectation of the product of the first $n - 1$ Hermite polynomials in a multivariate normal distribution with respect to the $n$ -th variable. A fresh perspective on the Kibble-Slepian formula