Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion II

TL;DR

This paper characterizes the distributional convergence of two subsequences of the signed cubic variation of fractional Brownian motion with Hurst parameter 1/6, advancing understanding of its asymptotic behavior.

Contribution

It provides a complete description of the convergence in distribution for two subsequences of the signed cubic variation of fractional Brownian motion with H=1/6.

Findings

Convergence in distribution of specific subsequences is fully characterized.

The results clarify the asymptotic behavior of the signed cubic variation.

Provides theoretical insights into fractional Brownian motion with H=1/6.

Abstract

The purpose of this paper is to provide a complete description the convergence in distribution of two subsequences of the signed cubic variation of the fractional Brownian motion with Hurst parameter $H = 1/6$.