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Penalized estimators for non linear inverse problems

Jean-Michel Loubes, Carenne Ludeña (2010)

ESAIM: Probability and Statistics

In this article we tackle the problem of inverse non linear ill-posed problems from a statistical point of view. We discuss the problem of estimating an indirectly observed function, without prior knowledge of its regularity, based on noisy observations. For this we consider two approaches: one based on the Tikhonov regularization procedure, and another one based on model selection methods for both ordered and non ordered subsets. In each case we prove consistency of the estimators and show...

Periodic solutions for a class of functional differential system

Weibing Wang, Baishun Lai (2012)

Archivum Mathematicum

In this paper, we study the existence of periodic solutions to a class of functional differential system. By using Schauder's fixed point theorem, we show that the system has aperiodic solution under given conditions. Finally, four examples are given to demonstrate the validity of our main results.

Periodic solutions for first order neutral functional differential equations with multiple deviating arguments

Lequn Peng, Lijuan Wang (2014)

Annales Polonici Mathematici

We consider first order neutral functional differential equations with multiple deviating arguments of the form ( x ( t ) + B x ( t - δ ) ) ' = g ( t , x ( t ) ) + k = 1 n g k ( t , x ( t - τ k ( t ) ) ) + p ( t ) . By using coincidence degree theory, we establish some sufficient conditions on the existence and uniqueness of periodic solutions for the above equation. Moreover, two examples are given to illustrate the effectiveness of our results.

Periodic solutions for n -th order delay differential equations with damping terms

Lijun Pan (2011)

Archivum Mathematicum

By using the coincidence degree theory of Mawhin, we study the existence of periodic solutions for n th order delay differential equations with damping terms x ( n ) ( t ) = i = 1 s b i [ x ( i ) ( t ) ] 2 k - 1 + f ( x ( t - τ ( t ) ) ) + p ( t ) . Some new results on the existence of periodic solutions of the investigated equation are obtained.

Periodic Solutions for Nonlinear Evolution Equations with Non-instantaneous Impulses

Michal Fečkan, JinRong Wang, Yong Zhou (2014)

Nonautonomous Dynamical Systems

In this paper, we consider periodic solutions for a class of nonlinear evolution equations with non-instantaneous impulses on Banach spaces. By constructing a Poincaré operator, which is a composition of the maps and using the techniques of a priori estimate, we avoid assuming that periodic solution is bounded like in [1-4] and try to present new sufficient conditions on the existence of periodic mild solutions for such problems by utilizing semigroup theory and Leray-Schauder's fixed point theorem....

Piecewise-polynomial signal segmentation using convex optimization

Pavel Rajmic, Michaela Novosadová, Marie Daňková (2017)

Kybernetika

A method is presented for segmenting one-dimensional signal whose independent segments are modeled as polynomials, and which is corrupted by additive noise. The method is based on sparse modeling, the main part is formulated as a convex optimization problem and is solved by a proximal splitting algorithm. We perform experiments on simulated and real data and show that the method is capable of reliably finding breakpoints in the signal, but requires careful tuning of the regularization parameters...

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