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Central limit theorem for the robust log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context
Central limit theorem the robust log-regression wavelet estimation
2010/11/23
In this paper, we study robust estimators of the memory parameter d of a (possibly) non stationary Gaussian time series with generalized spectral density f. This generalized spectral density is chara...
Asymptotic Limit of a Singularly Perturbed Stationary Diffusion Equation: The Case of a Limit Cycle
Diffusion Equation Limit Cycle
2010/11/23
A limit cycle for a nonlinear ordinary differential equation has a sustained, stationary oscillation in time; Any non-trivial stationary stochastic process also exhibits stationary oscillations in tim...
Limit cycle's uniqueness for second order O.D.E.'s polynomial in $\dot x$
Limit cycle's uniqueness O.D.E.'s polynomial
2010/11/12
We prove a uniqueness result for limit cycles of the second order ODE $\ddot x + \sum_{j=1}^{J}f_{j}(x)\dot x^{j} + g(x) = 0$. We extend a uniqueness result proved in \cite{CRV}. The main tool applied...
On the number of limit cycles in quadratic perturbations of quadratic codimension four centers
limit cycles quadratic codimension four centers
2010/11/15
This paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of quadratic codimension-four centers $Q_4$. Gavrilov and Iliev set an upper bound of {\it eight} for th...
We study a new family of "classical" orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with differential operators of Dunkl-type. These polynomials ...