Abstract : We define and study the multiparameter fractional Brownian motion. This process is a generalization of both the classical fractional Brownian motion and the multiparameter Brownian motion, when the condition of independence is relaxed. Relations with the Lévy fractional Brownian motion and with the fractional Brownian sheet are discussed. Different notions of stationarity of the increments for a multiparameter process are studied and applied to the fractional property. Using self-similarity we present a characterization for such processes. Finally, behavior of the multiparameter fractional Brownian motion along increasing paths is analysed.
Type de document :
Communication dans un congrès
Math Everywhere: deterministic and stochastic modelling in biomedicine, economics and industry, 2006, Italy. XVIII, pp.93-101, 2006
https://hal-ecp.archives-ouvertes.fr/hal-00652075
Contributeur : Erick Herbin
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Soumis le : mercredi 14 décembre 2011 - 18:11:52
Dernière modification le : jeudi 5 avril 2018 - 12:30:21
