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Central and non-central limit theorems for weighted power variations of fractional Brownian motion
dc.contributor.author | Nourdin, Ivan | |
dc.contributor.author | Nualart, David | |
dc.contributor.author | Tudor, Ciprian A. | |
dc.date.accessioned | 2015-03-09T21:40:11Z | |
dc.date.available | 2015-03-09T21:40:11Z | |
dc.date.issued | 2010-10-01 | |
dc.identifier.citation | Nourdin, Ivan., Nualart, David., Tudor, Ciprian A. "Central and non-central limit theorems for weighted power variations of fractional Brownian motion." Ann. Inst. H. Poincaré Probab. Statist. Volume 46, Number 4 (2010), 1055-1079. http://dx.doi.org/10.1214/09-AIHP342. | en_US |
dc.identifier.uri | http://hdl.handle.net/1808/17019 | |
dc.description | This is the published version, also available here: http://dx.doi.org/10.1214/09-AIHP342. | en_US |
dc.description.abstract | n this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q≥2 of the fractional Brownian motion with Hurst parameter H∈(0, 1), where q is an integer. The central limit holds for 1/2q<H≤1−1/2q, the limit being a conditionally Gaussian distribution. If H<1/2q we show the convergence in L2 to a limit which only depends on the fractional Brownian motion, and if H>1−1/2q we show the convergence in L2 to a stochastic integral with respect to the Hermite process of order q. | en_US |
dc.publisher | Annals of the Institute Henri Poincaré | en_US |
dc.subject | Fractional Brownian motion | en_US |
dc.subject | Central limit theorem | en_US |
dc.subject | Non-central limit theorem | en_US |
dc.subject | Hermite process | en_US |
dc.title | Central and non-central limit theorems for weighted power variations of fractional Brownian motion | en_US |
dc.type | Article | |
kusw.kuauthor | Nualart, David | |
kusw.kudepartment | Mathematics | en_US |
dc.identifier.doi | 10.1214/09-AIHP342 | |
kusw.oaversion | Scholarly/refereed, publisher version | |
kusw.oapolicy | This item meets KU Open Access policy criteria. | |
dc.rights.accessrights | openAccess |