ASYMPTOTIC BEHAVIOR OF WEIGHTED QUADRATIC AND CUBIC VARIATIONS OF FRACTIONAL BROWNIAN MOTION

• 成果类型: Article
• 署名作者: Nourdin, Ivan
• 署名单位: Universite Paris Cite; Sorbonne Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/07-AOP385
• 发表日期: 2008
• 页码: 2159-2175
• 关键词: CENTRAL LIMIT-THEOREMS; gaussian fields; functionals; CONVERGENCE

摘要

The present article is devoted to a fine study of the convergence of renormalized weighted quadratic and cubic variations of a fractional Brownian motion B with Hurst index H. In the quadratic (resp. Cubic) case, when H < 1/4 (resp. H < 1/6). we show by means of Malliavin Calculus that the convergence holds in L(2) toward in explicit limit which only depends on B. This result is somewhat surprising when compared with the celebrated Breuer and Major theorem.