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Absolute continuity, quadratic forms, and causal perturbations of product measures

Kanter M.

Probability and Mathematical Statistics

1999

Vol. 19, Fasc. 2

429--439

Necessary and sufficient conditions are given for the absolute continuity of a causally perturbed product measure with respect to the non-perturbed measure. When the perturbation is linear, these conditions involve the convergence of a quadratic form of independent random variables. The convergence of this form is studied when the independent random variables are symmetric or strictly stable.