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Multifractal Analysis of a Class of Additive Processes with Correlated Non-Stationary Increments
Electronic Journal of Probability
We consider a family of stochastic processes built from infinite sums of independent positive random functions on R + . Each of these functions increases linearly between two consecutive negative jumps, with the jump points following a Poisson point process on R + . The motivation for studying these processes stems from the fact that they constitute simplified models for TCP traffic on the Internet. Such processes bear some analogy with Lévy processes, but they are more complex in the sensedoi:10.1214/ejp.v9-208 fatcat:cxjtptbfurfyzbiky7f4z4gkki