On smooth behavior of probability distributions under polynomial mappings
Götze, Friedrich
Prokhorov, YV
Ulyanov, VV
characteristic functions
Cantor distribution
polynomials on random variables
singular distributions
Let X be a random variable with probability distribution P-X concentrated on [-1,1] and let Q(x) be a polynomial of degree k greater than or equal to 2. The characteristic function of a random variable Y = Q(X) is of order O(1/\t\(1/k)) as \t\ --> infinity if P-X is sufficiently smooth. In addition, for every epsilon: 1/k > epsilon > 0 there exists a singular distribution P-X such that every convolution P-X(n star) is also singular while the characteristic function of Y is of order O(1/\t\(1/k-epsilon)). While the characteristic function of X is small when "averaged," the characteristic function of the polynomial transformation Y of X is uniformly small.
SIAM PUBLICATIONS
1998
info:eu-repo/semantics/article
doc-type:article
text
https://pub.uni-bielefeld.de/record/1625472
Götze F, Prokhorov YV, Ulyanov VV. On smooth behavior of probability distributions under polynomial mappings. <em>THEORY OF PROBABILITY AND ITS APPLICATIONS</em>. 1998;42(1):28-38.
eng
info:eu-repo/semantics/altIdentifier/doi/10.1137/S0040585X97975927
info:eu-repo/semantics/altIdentifier/issn/0040-585X
info:eu-repo/semantics/altIdentifier/wos/000073918900003
info:eu-repo/semantics/closedAccess