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The Multiparameter Fractional Brownian Motion

In: Math Everywhere

Author

Listed:
  • Erick Herbin

    (Dassault Aviation)

  • Ely Merzbach

    (Bar Ilan University, Dept. of Mathematics)

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.

Suggested Citation

  • Erick Herbin & Ely Merzbach, 2007. "The Multiparameter Fractional Brownian Motion," Springer Books, in: Giacomo Aletti & Alessandra Micheletti & Daniela Morale & Martin Burger (ed.), Math Everywhere, pages 93-101, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-44446-6_8
    DOI: 10.1007/978-3-540-44446-6_8
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