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Convergence of scaled renewal processes and a packet arrival model. (English) Zbl 1043.60077
Authors’ summary: We study the superposition process of a class of independent renewal processes with long-range dependence. It is known that under two different scalings in time and space either fractional Brownian motion or a stable Lévy process may arise in the rescaling asymptotic limit. It is shown here that in a third, intermediate scaling regime a new limit process appears, which is neither Gaussian nor stable. The new limit process is characterized by its cumulant generating function and some of its properties are discussed.

MSC:
60K05 Renewal theory
60E07 Infinitely divisible distributions; stable distributions
60F05 Central limit and other weak theorems
60G18 Self-similar stochastic processes
60G52 Stable stochastic processes
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
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