LAUSR

Abstract Let B a , b be a weighted-fractional Brownian motion with indexes a and b satisfying | b | 1 ∧ ( 1 + a ) , a > − 1 which is a central Gaussian process such that E B t a , b B s a , b = 1 + b 2 ∫ 0 s ∧ t u a ( ( t − u ) b + ( s − u ) b ) d u . In this paper, we consider the asymptotic normality associated with processes ∫ 0 t B s + e a , b − B s a , b 2 − t a e 1 + b d s , t ∈ [ 0 , T ] , e > 0 . As an application we study the asymptotic normality of the estimator of parameter σ > 0 in stochastic process X t = σ B t a , b − β ∫ 0 t X s d s by using the generalized quadratic variation.