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Stable fractal sums of pulses: The cylindrical case. (English) Zbl 0844.60017
Summary: A class of $$\alpha$$-stable, $$0 < \alpha < 2$$, 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 $$H < 1/\alpha$$ 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.

##### MSC:
 60G18 Self-similar stochastic processes
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