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

Abstract EN

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.