DOI: 10.1142/s0218348x02000872. LARGE DEVIATIONS OF MULTIFRACTAL MEASURES

LARGE DEVIATIONS OF MULTIFRACTAL MEASURES

10.1142/s0218348x02000872

Crossref journal-article

World Scientific Pub Co Pte Lt

Fractals (219)

Abstract

We analyze the extremes of stationary multifractal measures using large deviation theory. We consider various cases involving discrete multiplicative cascades: scalar or vector cascades with dependent or independent generators, bare or dressed measures, and marginal (single-point) or joint (multi-point) extremes. In each case, we obtain the scaling behavior of the probability of large deviations as the resolution of the cascade diverges. Existing rough exponential limits for scalar cascades are confirmed, whereas for other cases our scaling relationships differ from previously published results. For scalar cascades, we refine the rough limits by obtaining the asymptotic pre-factor to the exponential term. Based on these refined asymptotics, we propose a variant to the Probability Distribution/Multiple Scaling (PDMS) technique to estimate the co-dimension function c(γ).

Bibliography

VENEZIANO, D. (2002). LARGE DEVIATIONS OF MULTIFRACTAL MEASURES. Fractals, 10(01), 117â129.

Authors 1

DANIELE VENEZIANO (first)

References 21 Referenced 10

10.1029/JD095iD03p01999
10.1142/S0218348X99000086
{'key': 'p_5', 'first-page': '84', 'volume': '198', 'author': 'Frish U.', 'journal-title': 'Elsevier North-Holland'} / Elsevier North-Holland by Frish U.
10.1029/JD092iD08p09693
10.1175/1520-0450(1993)032<0251:ASAOMR>2.0.CO;2
10.1017/S0022112074000711
10.1016/0001-8708(76)90151-1
10.1090/S0002-9947-96-01500-0
10.1103/PhysRevA.33.1141
{'key': 'p_13', 'first-page': '41', 'volume': '199', 'author': 'Schertzer D.', 'journal-title': 'Kluwer'} / Kluwer by Schertzer D.
{'key': 'p_14', 'first-page': '99', 'volume': '199', 'author': 'Lavallee D.', 'journal-title': 'Kluwer'} / Kluwer by Lavallee D.
10.1214/aoms/1177705674
10.1214/aop/1176993665
10.1214/aop/1176993239
10.1090/S0273-0979-1994-00521-X
10.1029/96JD01657
10.1137/1122003
10.1214/aop/1176993370
10.1214/aoms/1177704865
10.1016/S0022-1694(96)03086-7
{'key': 'p_32', 'first-page': '323', 'volume': '325', 'author': 'Benjoudi H.', 'year': '1997', 'journal-title': 'Surface Geosci. (Hydrol.)'} / Surface Geosci. (Hydrol.) by Benjoudi H. (1997)

Dates

Type	When
Created	22 years, 3 months ago (May 7, 2003, 12:18 a.m.)
Deposited	6 years ago (Aug. 7, 2019, 10:03 a.m.)
Indexed	1 year, 10 months ago (Oct. 17, 2023, 10:26 a.m.)
Issued	23 years, 5 months ago (March 1, 2002)
Published	23 years, 5 months ago (March 1, 2002)
Published Online	13 years, 3 months ago (April 30, 2012)
Published Print	23 years, 5 months ago (March 1, 2002)

Funders 0

None

BibTeX

@article{VENEZIANO_2002, title={LARGE DEVIATIONS OF MULTIFRACTAL MEASURES}, volume={10}, ISSN={1793-6543}, url={http://dx.doi.org/10.1142/s0218348x02000872}, DOI={10.1142/s0218348x02000872}, number={01}, journal={Fractals}, publisher={World Scientific Pub Co Pte Lt}, author={VENEZIANO, DANIELE}, year={2002}, month=mar, pages={117–129} }

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