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)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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- Luis G. Gorostiza & Reyla A. Navarro & Eliane R. Rodrigues, 2004. "Some Long-Range Dependence Processes Arising from Fluctuations of Particle Systems," RePAd Working Paper Series lrsp-TRS401, Département des sciences administratives, UQO.
- T. Bojdecki & Luis G. Gorostiza & A. Talarczyk, 2004. "Functional Limit Theorems for Occupation Time Fluctuations of Branching Systems in the Case of Long-Range Dependence," RePAd Working Paper Series lrsp-TRS402, Département des sciences administratives, UQO.
- Swanson, Jason, 2011. "Fluctuations of the empirical quantiles of independent Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 479-514, March.
- T. Bojdecki & Luis G. Gorostiza & A. Talarczyk, 2005. "A Long Range Dependence Stable Process and an Infinite Variance Branching System," RePAd Working Paper Series lrsp-TRS425, Département des sciences administratives, UQO.
- T. Bojdecki & Luis G. Gorostiza & A. Talarczyk, 2004. "Functional Limit Theorems for Occupation Time Fluctuations of Branching Systems in the Cases of Large and Critical Dimensions," RePAd Working Paper Series lrsp-TRS404, Département des sciences administratives, UQO.
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