On the estimation in a class of diffusion-type processes: application for diffusion Branching Processes

In this work a family of stochastic differential equations whose solutions are multidimensional diffusion-type (non necessarily markovian) processes is considered, and the estimation of a parametric vector ? which relates the coefficients is studied. The conditions for the existence of the likelihood function are proved and the estimator is obtained by continuously observing the process. An application for Diffusion Branching Processes is given. This problem has been studied in some special cases by Brown and Hewitt (1975), Liptser and Shiryayev (1978) and Sorensen (1983)