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

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Keywords

  • Fractional Brownian motion
  • Asymptotic
  • Independence
  • Local

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