The Annals of Probability

Dimension result and KPZ formula for two-dimensional multiplicative cascade processes

Xiong Jin

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We prove a Hausdorff dimension result for the image of two-dimensional multiplicative cascade processes, and we obtain from this result a KPZ-type formula which normally has one point of phase transition.

Article information

Ann. Probab., Volume 40, Number 1 (2012), 1-18.

First available in Project Euclid: 3 January 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G18: Self-similar processes 60G57: Random measures
Secondary: 28A78: Hausdorff and packing measures 28A80: Fractals [See also 37Fxx]

Hausdorff dimension image of stochastic process KPZ formula multiplicative cascade


Jin, Xiong. Dimension result and KPZ formula for two-dimensional multiplicative cascade processes. Ann. Probab. 40 (2012), no. 1, 1--18. doi:10.1214/10-AOP613.

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