Central limit theorems and parameter estimation associated with a weighted-fractional Brownian motion

- The paper studies Gaussian processes having not asymptotically stationary increments.
- The results generalize partially some known results about fractional Brownian motion.
- The paper constructs the estimator of the diffusion coefficient of an O-U model.
- The proposed method is shown to be robust to a large class of Gaussian processes.

Let Ba,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 EBta,bBsa,b=1+b2∫0s∧tua((t−u)b+(s−u)b)du.In this paper, we consider the asymptotic normality associated with processes ∫0tBs+εa,b−Bsa,b2−taε1+bds,t∈[0,T],ε>0.As an application we study the asymptotic normality of the estimator of parameter σ>0 in stochastic process Xt=σBta,b−β∫0tXsds by using the generalized quadratic variation.