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

Manuel Molina FernándezAurora 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...

Filtering of signals transmitted in multichannel from Chandrasekhar and Riccati recursions.

S. NakamoriA. HermosoJ. JiménezJ. Linares — 2005

Extracta Mathematicae

In this paper two recursive algorithms are proposed and compared as a solution of the least mean-squared error linear filtering problem of a wide-sense stationary scalar signal from uncertain observations perturbed by white and coloured additive noises. Considering that the state-space model of the signal is not available and that the variables modelling the uncertainty are not independent, the proposed algorithms are derived by using covariance information. The difference between both algorithms...

Quadratic estimation from non-independent uncertain observations with coloured noise.

S. NakamoriR. CaballeroA. HermosoJ. JiménezJ. Linares — 2004

Extracta Mathematicae

Recursive least-squares quadratic filtering and fixed-point smoothing algorithms for signal estimation from uncertain observations are derived when the uncertainty is modeled by not necessarily independent variables and the observations contain white plus coloured noise. The proposed estimators do not require the knowledge of the state-space of the model generating the signal, but only the moments, up to the fourth one, of the processes involved, along with the probability that the signal exists...

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

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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