Three Classes of Reaction-Diffusion Systems with Neumann Boundary Condition

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On some multivariate density estimates and empirical Bayes problems

This paper consider estimates of multidimensional density functions and their derivatives. The asymptotic unbiasedness and the convergence properties of these estimates are established.Some applications to empirical Bayes problems are considered.     

Nonparametric estimation of location parameter after a preliminary test on regression in the multivariate case

For a simple multivariate regression model, nonparametric estimation of the (vector of) intercept following a preliminary test on the regression vector is considered. Along with the asymptotic distribution of these estimators, their asymptotic bias and dispersion matrices are studied and allied efficiency results are presented.     

A note on asymptotic inference in a class of non-stationary processes

In this note some problems of asymptotic inference in a class of non-stationary stochastic processes are considered. In particular, it is shown that no criterion based on the existence of uniformly most powerful tests over a local neighborhood can be used in this situation.     

The Spearman footrule and a Markov chain property

An equivalent representation of the Spearman footrule is considered and a characterization in terms of a Markov chain is established. A martingale approach is thereby incorporated in the study of the asymptotic normality of the statistics.     

The Stationary Nonlinear Boltzmann Equation in a Couette Setting with Multiple, Isolated L q -solutions and Hydrodynamic Limits

This paper studies the stationary nonlinear Boltzmann equation for hard forces, in a Couette setting between two coaxial, rotating cylinders with given indata of Maxwellian type on the cylinders. A priori estimates are obtained mainly in L², leading to multiple, isolated solutions together with a hydrodynamic limit control, based on asymptotic expansions together with a rest term.     

Asymptotic stability of solitary wave solutions to the regularized long-wave equation

We study the asymptotic stability of solitary wave solutions to the regularized long-wave equation (RLW) in . RLW is an equation which describes the long waves in water. To prove the result, we make use of the monotonicity of the local H¹-norm and apply the Liouville property of (RLW) as in Merle and Martel (J. Math. Pures Appl. 79 (2000) 339; Arch. Rational Mech. Anal. 157 (2001) 219).