Bernoulli

  • Bernoulli
  • Volume 1, Number 3 (1995), 201-216.

Stable fractal sums of pulses: the cylindrical case

Renata Cioczek-Georges, Benoit B. Mandelbrot, Gennady Samorodnitsky, and Murad S. Taqqu

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Abstract

A class of α-stable, 0<α<2, processes is obtained as a sum of 'up-and-down' pulses determined by an appropriate Poisson random measure. Processes are H-self-affine (also frequently called 'self-similar') with H<1/α and have stationary increments. Their two-dimensional dependence structure resembles that of the fractional Brownian motion (for H<1/2), but their sample paths are highly irregular (nowhere bounded with probability 1). Generalizations using different shapes of pulses are also discussed.

Article information

Source
Bernoulli, Volume 1, Number 3 (1995), 201-216.

Dates
First available in Project Euclid: 29 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1193667815

Digital Object Identifier
doi:10.3150/bj/1193667815

Mathematical Reviews number (MathSciNet)
MR1363538

Zentralblatt MATH identifier
0844.60017

Keywords
measures of dependence path behaviour Poisson random measure self-affinity self-similarity stable processes stationarity of increments

Citation

Cioczek-Georges, Renata; Mandelbrot, Benoit B.; Samorodnitsky, Gennady; Taqqu, Murad S. Stable fractal sums of pulses: the cylindrical case. Bernoulli 1 (1995), no. 3, 201--216. doi:10.3150/bj/1193667815. https://projecteuclid.org/euclid.bj/1193667815


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