A general lower bound of parameter estimation for reflected Ornstein–Uhlenbeck processes

Abstract

A reflected Ornstein–Uhlenbeck process is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. It is an extended model of the traditional Ornstein–Uhlenbeck process being extensively used in finance as a one-factor short-term interest rate model. Under some mild conditions, this paper is devoted to the study of the analogue of the Cramer–Rao lower bound of a general class of parameter estimation of the unknown parameter in reflected Ornstein–Uhlenbeck processes.

Piecewise-Tunneled Captive Processes and Corridored Random Particle Systems

“…Similar principles, concerning the evolution of stochastic diffusions in restrictive conditions, are applied to population dynamic models as well (see [50,51]). Furthermore, the reader is guided to [52,53] for other recent developments.…”