Cioczek-Georges, RenataMandelbrot, Benoit B.Samorodnitsky, GennadyTaqqu, Murad S.2018-09-052018-09-051995-09Renata Cioczek-Georges, Benoit B Mandelbrot, Gennady Samorodnitsky, Murad S Taqqu. 1995. "Stable fractal sums of pulses: the cylindrical case." Bernoulli, Volume 1, pp. 201 - 216. https://doi.org/10.3150/bj/11936678151350-7265https://hdl.handle.net/2144/31179A class of α-stable, 0\textlessα\textless2, 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\textless1/α and have stationary increments. Their two-dimensional dependence structure resembles that of the fractional Brownian motion (for H\textless1/2), but their sample paths are highly irregular (nowhere bounded with probability 1). Generalizations using different shapes of pulses are also discussed.201 - 216© 1995 Bernoulli Society for Mathematical Statistics and ProbabilityStatisticsEconometricsStatistics & probabilityStable processesMeasures of dependencePath behaviourPoisson random measureSelf-affinitySelf-similarityStationarity of incrementsArticle0000-0002-1145-9082 (Taqqu, Murad S)