DOI: 10.1142/s0218348x99000086. BASIC PROPERTIES AND CHARACTERIZATION OF STOCHASTICALLY SELF-SIMILAR PROCESSES IN R<sup>d</sup>

BASIC PROPERTIES AND CHARACTERIZATION OF STOCHASTICALLY SELF-SIMILAR PROCESSES IN Rd

10.1142/s0218348x99000086

Crossref journal-article

World Scientific Pub Co Pte Lt

Fractals (219)

Abstract

The classical notion of self-similarity (ss) for random X(t) as invariance under the group of positive affine transformations {X→ arX, t→rt; ar>0} is extended by allowing ar to be a random variable. The resulting property of "stochastic self-similarity" (sss) is applied to both ordinary and generalized random processes in Rd, d≥1. The class of sss processes seems to correspond to that of multifractal processes (the latter are variously defined in the literature). The spectral measures of ordinary and generalized sss processes are themselves stochastically self-similar. Two characterizations of ss processes by Lamperti are extended to the sss case and several basic properties of ordinary and generalized sss processes are derived.

Bibliography

VENEZIANO, D. (1999). BASIC PROPERTIES AND CHARACTERIZATION OF STOCHASTICALLY SELF-SIMILAR PROCESSES IN Rd. Fractals, 07(01), 59â78.

Authors 1

DANIELE VENEZIANO (first)

References 12 Referenced 34

10.1146/annurev.fl.23.010191.002543
10.1175/1520-0450(1993)032<0251:ASAOMR>2.0.CO;2
10.1029/JD092iD08p09693
10.1090/S0002-9947-1962-0138128-7
{'key': 'p_12', 'first-page': '199', 'volume': '52', 'author': 'Vervaat W.', 'year': '1987', 'journal-title': 'Bull. Int. Statist. Inst.'} / Bull. Int. Statist. Inst. by Vervaat W. (1987)
{'key': 'p_13', 'first-page': '103', 'volume': '2', 'author': 'Maejima M.', 'year': '1989', 'journal-title': 'Sugaku Expositions'} / Sugaku Expositions by Maejima M. (1989)
{'key': 'p_15', 'first-page': '623', 'volume': '6', 'author': 'Schertzer D.', 'year': '1985', 'journal-title': 'Journal'} / Journal by Schertzer D. (1985)
{'key': 'p_16', 'first-page': '41', 'volume': '199', 'author': 'Schertzer D.', 'journal-title': 'Kluwer'} / Kluwer by Schertzer D.
10.1029/JD095iD03p01999
10.1029/94WR01791
10.1016/0378-4371(92)90446-W
10.1175/1520-0469(1993)050<0538:DRACTA>2.0.CO;2

Dates

Type	When
Created	22 years, 4 months ago (April 22, 2003, 7:50 a.m.)
Deposited	6 years ago (Aug. 6, 2019, 5:52 p.m.)
Indexed	1 year, 10 months ago (Oct. 17, 2023, 10:23 a.m.)
Issued	26 years, 6 months ago (March 1, 1999)
Published	26 years, 6 months ago (March 1, 1999)
Published Online	13 years, 9 months ago (Nov. 20, 2011)
Published Print	26 years, 6 months ago (March 1, 1999)

Funders 0

None

BibTeX

@article{VENEZIANO_1999, title={BASIC PROPERTIES AND CHARACTERIZATION OF STOCHASTICALLY SELF-SIMILAR PROCESSES IN Rd}, volume={07}, ISSN={1793-6543}, url={http://dx.doi.org/10.1142/s0218348x99000086}, DOI={10.1142/s0218348x99000086}, number={01}, journal={Fractals}, publisher={World Scientific Pub Co Pte Lt}, author={VENEZIANO, DANIELE}, year={1999}, month=mar, pages={59–78} }

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