Name
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. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.spa.2009.05.004 | Stochastic Processes and their Applications |
Keywords | Field | DocType |
60G15,(60G18,94A99,60H99) | Mathematical analysis,Stochastic process,Infinity,Sigma-algebra,Sigma,Local independence,Fractional Brownian motion,Mathematics | Journal |
Volume | Issue | ISSN |
119 | 10 | 0304-4149 |
Citations | PageRank | References |
1 | 0.43 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ilkka Norros | 1 | 613 | 86.52 |
| Eero Saksman | 2 | 158 | 30.82 |