Event Details

The reflected Ornstein-Uhlenbeck (ROU) process arises as the key approximating process for stochastic flow systems with reneging or balking customers/jobs. The ROU process can also be used to model interest rate, foreign exchange rate and even some asset price processes under market regulations. Our aim is to statistically estimate the key parameters of the system based on the (partially) observed data. In the first part of the talk, we assume the state process and its local time process are continuously observable until the observed Fisher information reaches a specified precision level. We derive the explicit formulas for the sequential maximum likelihood estimator and its mean squared error. The estimator is shown to be unbiased and uniformly normally distributed. In the second part of the talk, we assume that only the state process itself (not the local time process) is observable and the observations are made only at discrete time instants. Strong consistency and asymptotic normality are established. Our approach is of method-of-moments type and is based on the explicit form of the invariant density of the ROU process as well as its ergodicity. The method is valid irrespective of the length of the time intervals between consecutive observations.

Speaker: Chihoon Lee, Colorado State University

Slides: (TBA)