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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.

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.)
Full Text: DOI Euclid