Open Access
September 1995 Stable fractal sums of pulses: the cylindrical case
Renata Cioczek-Georges, Benoit B. Mandelbrot, Gennady Samorodnitsky, Murad S. Taqqu
Bernoulli 1(3): 201-216 (September 1995). DOI: 10.3150/bj/1193667815


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.


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Renata Cioczek-Georges. Benoit B. Mandelbrot. Gennady Samorodnitsky. Murad S. Taqqu. "Stable fractal sums of pulses: the cylindrical case." Bernoulli 1 (3) 201 - 216, September 1995.


Published: September 1995
First available in Project Euclid: 29 October 2007

zbMATH: 0844.60017
MathSciNet: MR1363538
Digital Object Identifier: 10.3150/bj/1193667815

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

Rights: Copyright © 1995 Bernoulli Society for Mathematical Statistics and Probability

Vol.1 • No. 3 • September 1995
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