Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case H=1/4

By Ivan Nourdin, Anthony R'eveillac. 2008

69 citations recorded by the source corpus.

We derive the asymptotic behavior of weighted quadratic variations of fractional Brow- nian 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.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/6c187a3838ea53b568d232953edae93a4a967878

How researchers see this paper

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In Finance

1. Alexandra Chronopoulou
2. Frederi G. Viens
3. Ciprian A. Tudor
4. Ivan Nourdin
5. T. T. Diu Tran
6. David Nualart
7. Murad S. Taqqu
8. Yaozhong Hu

In Management Science and Operations Research

1. Ciprian A. Tudor
2. Alexandra Chronopoulou
3. Frederi G. Viens

Citations in the corpus

• Self-similarity parameter estimation and reproduction property for non-Gaussian Hermite processes (2008, background): “Lastly, we mention that various very recent and interesting results, which are beyond the scope of this article, have been proven for weighted power variations of stochastic processes such as fractional Brownian motion (see [11], [14], [13]), fractional Brownian sheets (see [18]), iterated Brownian ”