AN APPROXIMATE MAXIMUM LIKELIHOOD ESTIMATOR OF DRIFT PARAMETERS IN A MULTIDIMENSIONAL DIFFUSION MODEL

For a fixed T and k > 2, a k-dimensional vector stochastic differential equation dX(t) = mu (X-t,theta ) dt + nu ( X- t ) dW(t), t , is studied over a time interval [0, , T ]. Vector of drift parameters 9 is unknown. The dependence in 9 is in <= eneral nonlinear. We prove that the difference between approximate maximum likelihood estimator of the drift parameter theta(n)- theta(nT) obtained from discrete observations ( X (i) triangle( n) , 0 <= i <= n ) and maximum likelihood estimator 9 - 9 T obtained from continuous observations ( X-t , 0 <= t <= T ), when triangle(n)= n = T/n tends to zero, conver <= es stably in law to the mixed normal random vector with covariance matrix that depends on 9 and on path ( X (t ), 0 <= t <= T ). The uniform ellipticity of diffusion matrix S ( x ) = nu ( x ) nu ( x ) T emerges as the main assumption on the diffusion coefficient function.