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.
"Stable fractal sums of pulses: the cylindrical case." Bernoulli 1 (3) 201 - 216, September 1995. https://doi.org/10.3150/bj/1193667815