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Remarks on Confidence Intervals for Self-Similarity Parameter of a Subfractional Brownian Motion

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  • Junfeng Liu
  • Litan Yan
  • Zhihang Peng
  • Deqing Wang

Abstract

We first present two convergence results about the second-order quadratic variations of the subfractional Brownian motion: the first is a deterministic asymptotic expansion; the second is a central limit theorem. Next we combine these results and concentration inequalities to build confidence intervals for the self-similarity parameter associated with one-dimensional subfractional Brownian motion.

Suggested Citation

  • Junfeng Liu & Litan Yan & Zhihang Peng & Deqing Wang, 2012. "Remarks on Confidence Intervals for Self-Similarity Parameter of a Subfractional Brownian Motion," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, January.
    • Handle: RePEc:hin:jnlaaa:804942
    DOI: 10.1155/2012/804942
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    Cited by:

    1. Kęstutis Kubilius & Dmitrij Melichov, 2016. "Exact Confidence Intervals of the Extended Orey Index for Gaussian Processes," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 785-804, September.

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