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

• Autorzy: Kanter M.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

absolute continuity of measures; quadratic forms; stable random variables; symmetric random variables; product measures

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1999
• Tom: Vol. 19, Fasc. 2
• Strony: 429--439
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Kanter M.

• 1216 Monterey Avenue, Berkeley, California 94707, USA

Bibliografia

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• [2] W. Feller, An Introduction to Probability Theory and Its Applications 2, 2nd edition, Wiley, New York 1971.
• [3] T. T. Kadota and L. A. Shepp, Conditions for absolute continuity between a certain pair of probability measures, Z. Wahrscheinlichkeitstheorie verw. Gebiete 16 (1970), pp. 250-260.
• [4] J.-P. Kahane, Some Random Series of Functions, D. C. Heath & Co., Lexington, Mass., 1968.
• [5] M. Kanter, On distinguishing translates of measures, Ann. Math. Statist. 40 (1969), pp. 1773-1777.
• [6] - Correction to "On distinguishing translates of measures”, Ann. Probab. 3 (1975), pp. 189-190.
• [7] - Equivalence singularity dichotomies for a class of ergodic measures, Math. Proc. Cambridge Philos. Soc. 81 (1977), pp. 249-252.
• [8] W. Linde, Probability in Banach Spaces. Stable and Infinitely Divisible Distributions, Wiley, New York 1986.
• [9] L. A. Shepp, Distinguishing a sequence of random variables from a translate of itself, Ann. Math Statist. 36 (1965), pp. 1107-1112.
• [10] A. N. Shiryayev, Probability, Springer, New York 1984.