Dimension results and KPZ formula for two dimensional multiplicative cascade process

Mathematics – Probability

Scientific paper

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31 pages

Scientific paper

We prove a Hausdorff dimension result for the image of two dimensional multiplicative cascade process, and we obtain from this result a KPZ-like formula that normally has one point of phase transition. We also prove that this Hausdorff dimension result holds almost surely for all Borel sets if and only if the process is fractional with unique parameter. The "only if" part relies on the multifractal analysis of the process and a level set dimension result.

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