ABSOLUTE CONTINUITY, QUADRATIC FORMS, AND CAUSAL
PERTURBATIONS OF PRODUCT MEASURES
Abstract: 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.
1991 AMS Mathematics Subject Classification: Primary: 60B10, 60B11.
Key words and phrases: Absolute continuity of measures, quadratic forms, stable
random variables, symmetric random variables, product measures.