Drift parameter estimation for tempered fractional Ornstein–Uhlenbeck processes based on discrete observations - Prykhodko, Olha; Ralchenko, Kostiantyn (VTeX, 2026)
The problem of estimating the drift parameter is considered for an Ornstein–Uhlenbeck-type process driven by a tempered fractional Brownian motion (tfBm) or tempered fractional Brownian motion of the second kind (tfBmII). Unlike most existing studies, which assume continuous-time observations, a more realistic setting of discrete-time data is in focus. The strong consistency of a discretized least squares estimator is established under an asymptotic regime where the observation interval tends to zero while the total time horizon increases. A key step in the analysis involves deriving almost sure upper bounds for the increments of both tfBm and tfBmII.
Keywords: Tempered fractional process; asymptotic growth; Langevin equation; least squares estimator; discretization; strong consistency; fi=Matemaattiset tieteet|en=Mathematics|