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arXiv · 1604.03328

Local fluctuations of critical Mandelbrot cascades

Dariusz Buraczewski·Piotr Dyszewski·Konrad Kolesko
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Abstract

We investigate so-called generalized Mandelbrot cascades at the freezing (critical) temperature. It is known that, after a proper rescaling, a~sequence of multiplicative cascades converges weakly to some continuous random measure. Our main question is how the limiting measure $\mu$ fluctuates. For any given point $x$, denoting by $B_n(x)$ the ball of radius $2^{-n}$ centered around $x$, we present optimal lower and upper estimates of $\mu(B_n(x))$ as $n \to \infty$.

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Dariusz Buraczewski, Piotr Dyszewski, Konrad Kolesko. 2016-04-12. Local fluctuations of critical Mandelbrot cascades. https://arxiv.org/abs/1604.03328

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