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Generators of Feller semigroups with coefficients depending on parameters and optimal estimators. (English) Zbl 1152.47032
This paper follows one Feller’s classical boundary theory on the realization of semigroups of one-dimensional elliptic operators to the special operators with diffusion coefficient of power function \(x^{2 \alpha}\) and drift \(a x^{2 \alpha -1}+ \theta x^ \alpha \) on the interval \((0, + \infty)\) under Wentzell’s boundary conditions. The most interesting part is for the GMM estimation (Generalized Method of Moments by L. P. Hansen) of parameters \(\alpha\) and \(\theta\), knowing \(n_T\) values of the diffusion processes at \(n_T\) fixed times, in the special case of \( \alpha = 1/2\), which is connected to financial mathematics. A simulation study of the estimators is performed by discrete approximation of the SDEs and the simulation results obtained are discussed in the paper.
47D07 Markov semigroups and applications to diffusion processes
60J60 Diffusion processes
62M05 Markov processes: estimation; hidden Markov models
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
91B70 Stochastic models in economics
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