The Annals of Probability

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

Xiong Jin

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Abstract

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

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

Dates
First available in Project Euclid: 3 January 2012

Permanent link to this document
https://projecteuclid.org/euclid.aop/1325604995

Digital Object Identifier
doi:10.1214/10-AOP613

Mathematical Reviews number (MathSciNet)
MR2917765

Zentralblatt MATH identifier
1298.60046

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

Keywords
Hausdorff dimension image of stochastic process KPZ formula multiplicative cascade

Citation

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. https://projecteuclid.org/euclid.aop/1325604995


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References

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