In this paper we present an alternative to the Gaussian and Cauchy distributions for modeling stochastic signals. The proposed model has the same impulsiveness as the Cauchy density, but it is derived as a sub-Gaussian process, i.e., a variance mixture of Gaussian random variables. We proceed to use the derived model in the problem of signal parameter estimation through the use of multisensor d...

We focus on eventually non-linear abstract Cauchy problems with a generalized fractional derivative in time. First we prove local existence and uniqueness result, then Grönwall inequality. Before addressing the inequality, study some properties of eigenvalues eigenfunctions derivatives. Finally, consequences

In this paper, we consider the inverse problem for the Laplace equation in two-dimensions which requires the determination of the location, size and shape of an unknown, or partially unknown, portion @ of the boundary @ of a solution domain R from additional Cauchy data on the remaining portion of the boundary 1⁄4 @ . This problem arises in the study of quantitative non-destructive evaluation o...

The present paper concerns with the global structure and asymptotic behavior of the discontinuous solutions to flood wave equations. By solving a free boundary problem, we first obtain the global structure and large time behavior of the weak solutions containing two shock waves. For the Cauchy problem with a class of initial data, we use Glimm scheme to obtain a uniform BV estimate both with re...

We draw here on the relation between the Cauchy and hyperbolic secant distributions to prove that the MLE of the scale parameter of Cauchy distribution is log-normally distributed and to study the properties of a Hodges-Lehmann type estimator for the scale parameter. This scale estimator is slightly biased but performs well even on small samples regardless of the location parameter. The asympto...