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.


60G18 Self-similar stochastic processes
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