Local independence of fractional Brownian motion

Ilkka Norros (Corresponding Author), Eero Saksman

    Research output: Contribution to journalArticleScientificpeer-review

    2 Citations (Scopus)

    Abstract

    Let σ(t,t′) be the sigma-algebra generated by the differences Xs−Xs′ with s,s′∈(t,t′), where (Xt)−∞<t<∞ is the fractional Brownian motion with Hurst index H∈(0,1). We prove that for any two distinct timepoints t1 and t2 the sigma-algebras σ(t1−ε,t1+ε) and σ(t2−ε,t2+ε) are asymptotically independent as ε↘0. We show the independence in the strong sense that Shannon’s mutual information between the two σ-algebras tends to zero as ε↘0. Some generalizations and quantitative estimates are also provided.
    Original languageEnglish
    Pages (from-to)3155 - 3172
    Number of pages18
    JournalStochastic Processes and their Applications
    Volume119
    Issue number10
    DOIs
    Publication statusPublished - 2009
    MoE publication typeA1 Journal article-refereed

    Keywords

    • Fractional Brownian motion
    • Asymptotic
    • Independence
    • Local

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