Lognormal $${\star}$$ -scale invariant random measures
نویسندگان
چکیده
منابع مشابه
Lognormal scale invariant random measures
In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with lognormal weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned continuous equation; these measures fall under the scope of the Gaussian multiplicative chaos theory developed by J....
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Proof. We will prove the general case of conditional dependence measure since the other case follows trivially as a special case when Z = ∅. The kernel-free property of the dependence measures is used to prove the result. The proof essentially uses change of variables formulas for transformation of random variables. From Theorem 1, we have
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2012
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-012-0412-9