Asymptotic expansion in approximation by normal law

Abstract

We consider the asymptotic behavior of the convolution P*n(A\sqrt{n}) of a k-dimensional probability distribution P(A) as n \to \infty for A from the \sigma-algebra M of Borel subsets of Euclidian space Rk or from its subclasses.

Keywords

• probability distributions in R^k,
• convolutions
• Bergström identity
• Appell polynomials
• Chebyshev–Cramer asymptotic expansion