Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)

Consider an Ornstein-Uhlenbeck process, $dX_t=- heta X_t dt+sigma dB^H_t$, driven by fractional Brownian motion B^H with known Hurst parameter Hge 1/2 and known variance sigma but with unknown parameter heta>0. Assume that the process is observed at discrete time instants t=h, 2h, ..., nh. We construct an estimator hat heta_n of heta which is strongly consistent, namely, widehat { heta}_n converges to heta almost surely as n goes to infinity. We also obtain a central limit type and a Berry-Esseen type theorem for this estimator when 1/2 le H<3/4. The tool we use is some recent result of central limit theorem for multiple Wiener integrals through Malliavin calculus.

Speaker: Jian Song, Rutgers University