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# A class of cylindrical pulse processes

**Renata Cioczek-Georges
**

Benoit B. Mandelbrot

Gennady Samorodnitsky

Murad S. Taqqu

### Abstract:

*A class of -stable, , 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 and have stationary increments. Their two-dimensional
dependence structure resembles that of the fractional Brownian motion (for
), but their sample paths are highly irregular (nowhere
bounded with probability 1). Generalizations using different shapes
of pulses are also discussed.
*
*