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On the estimation in a class of diffusion-type processes. Aplication for diffusion branching processes.

Manuel Molina Fernández;  Aurora Hermoso Carazo — 1990

Extracta Mathematicae

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 θ 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...

On the estimation of the drift coefficient in diffusion processes with random stopping times.

Ramón Gutiérrez Jáimez;  Aurora Hermoso Carazo;  Manuel Molina Fernández — 1986

Trabajos de Estadística

This paper considers stochastic differential equations with solutions which are multidimensional diffusion processes with drift coefficient depending on a parametric vector θ. By considering a trajectory observed up to a stopping time, the maximum likelihood estimator for θ has been obtained and its consistency and asymptotic normality have been proved.

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