Asymptotic behavior of weighted power variations of fractional Brownian motion in Brownian time
Raghid Zeineddine
TL;DR
This paper investigates the long-term behavior of weighted power variations of a process formed by composing fractional Brownian motion with Brownian motion, revealing insights into their asymptotic properties.
Contribution
It provides new theoretical results on the asymptotic behavior of weighted power variations for fractional Brownian motion in Brownian time, a less explored area.
Findings
Characterization of asymptotic limits of weighted power variations
Extension of existing theories to fractional Brownian motion in Brownian time
Potential applications in stochastic analysis and modeling
Abstract
We study the asymptotic behavior of weighted power variations of fractional Brownian motion in Brownian time Z_t:= X_{Y_t}, t >= 0, where X is a fractional Brownian motion and Y is an independent Brownian motion.
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