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 language | English |
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Pages (from-to) | 3155 - 3172 |
Number of pages | 18 |
Journal | Stochastic Processes and their Applications |
Volume | 119 |
Issue number | 10 |
DOIs | |
Publication status | Published - 2009 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Fractional Brownian motion
- Asymptotic
- Independence
- Local