ASYMPTOTIC BEHAVIOR OF WEIGHTED QUADRATIC VARIATIONS OF FRACTIONAL BROWNIAN MOTION: THE CRITICAL CASE H=1/4

• 成果类型: Article
• 署名作者: Nourdin, Ivan; Reveillac, Anthony
• 署名单位: Sorbonne Universite; Universite Paris Cite; Humboldt University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP473
• 发表日期: 2009
• 页码: 2200-2230
• 关键词: CENTRAL LIMIT-THEOREMS; gaussian fields; itos formula; hurst index; sdes driven; CONVERGENCE; functionals

摘要

We derive the asymptotic behavior of weighted quadratic variations of fractional Brownian motion B with Hurst index H = 1/4. This completes the only missing case in a very recent work by I. Nourdin, D. Nualart and C. A. Tudor. Moreover, as an application, we solve a recent conjecture of K. Burdzy and J. Swanson on the asymptotic behavior of the Riemann sums with alternating signs associated to B.