We consider the asymptotic properties of the superpositions of independent renewal processes with long-range dependence whose distributions belong to a finite set of different distributions. In fact it is so called Gnedenko problem but in new setting. We describe the conditions under which we have the convergence to limit process which is pseudostable Levy Motion. Such process has the property of stochastic periodicity. Our results are the extensions of the results by M. Taqqu and Levy (1986, 2000), Mikosch and et al. (2002)
Approximation of network traffic by pseudostable Levy motion
D'APICE, Ciro;MANZO, Rosanna;
2004
Abstract
We consider the asymptotic properties of the superpositions of independent renewal processes with long-range dependence whose distributions belong to a finite set of different distributions. In fact it is so called Gnedenko problem but in new setting. We describe the conditions under which we have the convergence to limit process which is pseudostable Levy Motion. Such process has the property of stochastic periodicity. Our results are the extensions of the results by M. Taqqu and Levy (1986, 2000), Mikosch and et al. (2002)File in questo prodotto:
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