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.
Publié le : 1995-09-14
Classification:
measures of dependence,
path behaviour,
Poisson random measure,
self-affinity,
self-similarity,
stable processes,
stationarity of increments
@article{1193667815,
author = {Cioczek-Georges, Renata and Mandelbrot, Benoit B. and Samorodnitsky, Gennady and Taqqu, Murad S.},
title = {Stable fractal sums of pulses: the cylindrical case},
journal = {Bernoulli},
volume = {1},
number = {3},
year = {1995},
pages = { 201-216},
language = {en},
url = {http://dml.mathdoc.fr/item/1193667815}
}
Cioczek-Georges, Renata; Mandelbrot, Benoit B.; Samorodnitsky, Gennady; Taqqu, Murad S. Stable fractal sums of pulses: the cylindrical case. Bernoulli, Tome 1 (1995) no. 3, pp. 201-216. http://gdmltest.u-ga.fr/item/1193667815/