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

Xiong Jin

doi:10.1214/10-AOP613

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

Research output: Contribution to journal › Article › peer-review

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. © 2012 Institute of Mathematical Statistics.

Original language	English
Pages (from-to)	1-18
Number of pages	17
Journal	Annals of Probability
Volume	40
Issue number	1
DOIs	https://doi.org/10.1214/10-AOP613
Publication status	Published - Jan 2012

Keywords

Hausdorff dimension
Image of stochastic process
KPZ formula
Multiplicative cascade

Access to Document

10.1214/10-AOP613

Cite this

@article{d420afb9a5b94ca49e744b4cd15206dd,

title = "Dimension result and KPZ formula for two-dimensional multiplicative cascade processes",

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. {\textcopyright} 2012 Institute of Mathematical Statistics.",

keywords = "Hausdorff dimension, Image of stochastic process, KPZ formula, Multiplicative cascade",

author = "Xiong Jin",

year = "2012",

month = jan,

doi = "10.1214/10-AOP613",

language = "English",

volume = "40",

pages = "1--18",

journal = "Annals of Probability",

issn = "0091-1798",

publisher = "Institute of Mathematical Statistics",

number = "1",

}

TY - JOUR

T1 - Dimension result and KPZ formula for two-dimensional multiplicative cascade processes

AU - Jin, Xiong

PY - 2012/1

Y1 - 2012/1

N2 - 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. © 2012 Institute of Mathematical Statistics.

AB - 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. © 2012 Institute of Mathematical Statistics.

KW - Hausdorff dimension

KW - Image of stochastic process

KW - KPZ formula

KW - Multiplicative cascade

U2 - 10.1214/10-AOP613

DO - 10.1214/10-AOP613

M3 - Article

SN - 0091-1798

VL - 40

SP - 1

EP - 18

JO - Annals of Probability

JF - Annals of Probability

IS - 1

ER -

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

Abstract

Keywords

Access to Document

Fingerprint

Cite this