The problem of aggregating different stochastic process into a unique one that must be characterized based on the statistical knowledge of its components is a key point in the modeling of many complex phenomena such as the merging of traffic flows at network nodes. Depending on the physical intuition on the interaction between the processes, many different aggregation policies can be devised, from averaging to taking the maximum in each time slot. We here address flows averaging and maximum since they are very common modeling options. Then we give a set of axioms defining a general aggregation operator and, based on some advanced results of functional analysis, we investigate how the decay of correlation of the original processes affect the decay of correlation (and thus the self-similar features) of the aggregated process.
On the aggregation of self-similar processes / G., Mazzini; R., Rovatti; Setti, G.. - In: IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS, COMMUNICATIONS AND COMPUTER SCIENCES. - ISSN 0916-8508. - STAMPA. - E88-A:10(2005), pp. 2656-2663. [10.1093/ietfec/e88-a.10.2656]
On the aggregation of self-similar processes
SETTI G.
2005
Abstract
The problem of aggregating different stochastic process into a unique one that must be characterized based on the statistical knowledge of its components is a key point in the modeling of many complex phenomena such as the merging of traffic flows at network nodes. Depending on the physical intuition on the interaction between the processes, many different aggregation policies can be devised, from averaging to taking the maximum in each time slot. We here address flows averaging and maximum since they are very common modeling options. Then we give a set of axioms defining a general aggregation operator and, based on some advanced results of functional analysis, we investigate how the decay of correlation of the original processes affect the decay of correlation (and thus the self-similar features) of the aggregated process.Pubblicazioni consigliate
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https://hdl.handle.net/11583/2696605
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