The Multiparameter Fractional Brownian Motion

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.
Document type :
Conference papers
Complete list of metadatas

https://hal-ecp.archives-ouvertes.fr/hal-00652075
Contributor : Erick Herbin <>
Submitted on : Wednesday, December 14, 2011 - 6:11:52 PM
Last modification on : Friday, July 26, 2019 - 2:14:28 PM

Links full text

Identifiers

Collections

Citation

Erick Herbin, Ely Merzbach. The Multiparameter Fractional Brownian Motion. Math Everywhere: deterministic and stochastic modelling in biomedicine, economics and industry, 2006, Italy. pp.93-101. ⟨hal-00652075⟩

Share

Metrics

Record views

186