Continuity in law with respect to the Hurst index of some additive functionals of sub-fractional Brownian motion. Issue 4 (4th July 2017)

• Record Type: Journal Article
• Authors: Ouahra, M. Ait; Sghir, A.
• Is Part Of: Stochastic analysis and applications. Volume 35:Issue 4(2017)
• Page Start: 677
• Page End: 690
• Publication Date: 2017-07-04
• Subjects: Anisotropic Besov spaces -- limit theorem -- tightness -- continuity in law -- fractional Brownian motion -- sub-fractional Brownian motion -- local time -- fractional derivative -- slowly varying function; 2010 -- 46E30 -- 60B12; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2017.1309979
• Languages: English
• ISSNs: 0736-2994

Abstract

ABSTRACT: In this article, first, we prove some properties of the sub-fractional Brownian motion introduced by Bojdecki et al. [ Statist. Probab. Lett. 69(2004):405–419]. Second, we prove the continuity in law, with respect to small perturbations of the Hurst index, in some anisotropic Besov spaces, of some continuous additive functionals of the sub-fractional Brownian motion. We prove that our result can be obtained easily, by using the decomposition in law of the sub-fractional Brownian motion given by Bardina and Bascompte [ Collect. Math. 61(2010):191–204] and Ruiz de Chavez and Tudor [ Math. Rep. 11(2009):67–74], without using the result of Wu and Xiao [ Stoch. Proc. Appl. 119(2009):1823–1844] by connecting the sub-fractional Brownian motion to its stationary Gaussian process through Lamperti's transform. This decomposition in law leads to a better understanding and simple proof of our result.