Articlegold2012

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

Junfeng Liu · Litan Yan · Zhihang Peng · Deqing Wang

18 citations0/0 files storedAbstract and Applied Analysis

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Stochastic processes and financial applications Stochastic processes and statistical mechanics Fractional Differential Equations Solutions

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.

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References

2001Stochastic Calculus with Respect to Gaussian Processes 1997THE MALLIAVIN CALCULUS AND RELATED TOPICS (Probability and its Applications)2008Stein’s method on Wiener chaos 2006Some properties of the sub-fractional Brownian motion 2009Density Formula and Concentration Inequalities with Malliavin Calculus 2007Variations and estimators for the selfsimilarity order through Malliavin calculus 2008On the Wiener integral with respect to a sub-fractional Brownian motion on an interval 2009On the collision local time of sub-fractional Brownian motions

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