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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 19, Fasc. 2,
pages 429 - 439
 

ABSOLUTE CONTINUITY, QUADRATIC FORMS, AND CAUSAL PERTURBATIONS OF PRODUCT MEASURES

Marek Kanter

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.

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