MINIMUM CONTRAST ESTIMATION IN DIFFUSION PROCESSES

A study is made of the asymptotic theory of estimates of an unknown parameter in continuous-time Markov processes, which are described by nonlinear stochastic differential equations. The maximum likelihood estimate and the minimum contrast estimate are investigated. For these estimates, strong consistency and asymptotic normality are proved. The unknown parameter is assumed to take its values either in an open or in a compact set of real numbers.