Central limit theorem for weighted local time of L2L2 modulus of fractional Brownian motion

In this paper, we mainly prove a central limit theorem for weighted local time of L2L2-modulus of fractional Brownian motion with Hurst parameter H∈(12,1). Similar to Hu and Nualart (2009), based on techniques of stochastic analysis, the main ingredients of the proof are analogous to the asymptotic version of Knight’s theorem and the fractional Clark–Ocone formula for the L2L2-modulus of the weighted local time increments.