Sub-fractional Brownian motion and its relation to occupation times
AbstractWe study a long-range dependence Gaussian process which we call “sub-fractional Brownian motion” (sub-fBm), because it is intermediate between Brownian motion (Bm) and fractional Brownian motion (fBm) in the sense that it has properties analogous to those of fBm, but the increments on non-overlapping intervals are more weakly correlated and their covariance decays polynomially at a higher rate. Sub-fBm has a parameter h E (0, 2), we show how it arises from occupation time fluctuations of branching particle systems for h >= 1 and we exhibit the long memory effect of the initial condition.
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Bibliographic InfoPaper provided by Département des sciences administratives, UQO in its series RePAd Working Paper Series with number lrsp-TRS376.
Length: 14 pages
Date of creation: 15 Jun 2004
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Long-range dependence; Fractional Brownian motion; Sub-fractional Brownian motion; Occupation time fluctuations; Branching systems.;
Find related papers by JEL classification:
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-05-14 (All new papers)
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