Parameters estimation of continuous-time bilinear processes with a reflected boundary

Diffusion processes for modeling, among other fields, (macro-) econometrics, mathematical finance, biology, queueing, and electrical engineering often involve reflection at one or two barriers in order to restrict the state space of the process, which returns continuously and immediately to the interior of the state space when it attains a one-sided barrier. In this paper, we investigate the L2 structure and estimation of such processes. The methodology of estimation is built upon the least squares (LS) approach for one-dimensional continuous-time ergodic reflected bilinear (RCOBL) processes. Our estimation procedure is based on continuously and/or discretely observed processes. So, We provide expressions for the moments up to the n-th order and derive explicit formulas for the parameter estimates involved in the process. EquationAA dX~(t)=m(X~(t))dt+σλ(X~(t))dW(t)+dL(t).A dditionally, we establish the strong consistency and asymptotic normality (CAN) of the parameters estimates. Numerical results and empirical analysis are proposed to illustrate our theory.