Estimation in Interacting Diffusions: Continuous and Discrete Sampling

Abstract

Consistency and asymptotic normality of the sieve estimator and an approximate maximum likelihood estimator of the drift coefficient of an interacting particles of diffusions are studied. For the sieve estimator, observations are taken on a fixed time interval [0,<i>T</i>] and asymptotics are studied as the number of interacting particles increases with the dimension of the sieve. For the approximate maximum likelihood estimator, discrete observations are taken in a time interval [0,<i>T</i>] and asymptotics are studied as the number of interacting particles increases with the number of observation time points.