Estimation of parameters in linear diffusion models (Q1406451)

On some probability space \((\Omega,F,P)\) let the random process \( X = (X_t)_{t\geq 0} \) with the stochastic differential \[ dX_t = (a+bX_t) dt + X_t dw_t,\quad X_0 = x_0,\quad t\geq 0, \] be observed, where \(a\) and \(b\) are unknown parameters, \( w = (w_t)_{t\geq 0} \) is a standard real process. The asymptotic properties of the parameter estimates are studied which are obtained by the method of maximum likelihood. Moreover, two types of observation are considered continuous and discrete ones.