Related papers: Identification and well-posedness in a class of no…
For many years, image over-segmentation into superpixels has been essential to computer vision pipelines, by creating homogeneous and identifiable regions of similar sizes. Such constrained segmentation problem would require a clear…
In this paper, we study the Cauchy problem of the Euler-Nernst-Planck-Possion system. We obtain global well-posedness for the system in dimension $d=2$ for any initial data in $H^{s_1}(\mathbb{R}^2)\times H^{s_2}(\mathbb{R}^2)\times…
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show…
There is a tendency to write the equations of general relativity as a first order symmetric system of time dependent partial differential equations. However, for numerical reasons, it might be advantageous to use a second order formulation…
In this paper we prove well-posedness and stabibility of a class of stochastic delay differential equations with singular drift. Moreover, we show local well-posedness under localized assumptions.
We consider the well-posedness of a class of hyperbolic partial differential equations on a one dimensional spatial domain. This class includes in particular infinite-dimensional networks of transport, wave and beam equations, or even…
In this paper, we deal with the parabolic KWC system, associated with the mathematical model of grain boundary motion. The goal of this paper is to guarantee the well-posedness of the parabolic KWC system. However, such results have not…
In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements.…
Cognitive diagnosis models have been popularly used in fields such as education, psychology, and social sciences. While parametric likelihood estimation is a prevailing method for fitting cognitive diagnosis models, nonparametric…
Identifiability is a desirable property of a statistical model: it implies that the true model parameters may be estimated to any desired precision, given sufficient computational resources and data. We study identifiability in the context…
We review $H^{1}$-well-posedness for initial value problems of ordinary differential equations with state-dependent right-hand side. We streamline known approaches to infer existence and uniqueness of solutions for small times given a…
In this paper we consider well-posedness properties of vector optimization problems with objective function $f: X \to Y$ where $X$ and $Y$ are Banach spaces and $Y$ is partially ordered by a closed convex pointed cone with nonempty…
It is well-known that every convex function admits an affine support at every interior point of a domain. Convex functions of higher order (precisely of an odd order) have a similar property: they are supported by the polynomials of degree…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
We consider a diffusion process on the edges of a finite network and allow for feedback effects between different, possibly non-adjacent edges. This generalizes the setting that is common in the literature, where the only considered…
An ill-posed inverse problem of autoconvolution type is investigated. This inverse problem occurs in nonlinear optics in the context of ultrashort laser pulse characterization. The novelty of the mathematical model consists in a physically…
We establish the global well-posedness of the $D(A)-$valued strong solution to a nonlinear heat equation with constraints on a \textit{Poincar\'e domain} $\bO\subset \R^d$ whose boundary is of class $C^2$. Consider the following nonlinear…
We investigate the Cauchy problem for a nonlocal (two-place) FORQ equation. By interpreting this equation as a special case of a two-component peakon system (exhibiting a cubic nonlinearity), we convert the Cauchy problem into a system of…
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…
This paper considers nonparametric identification and estimation of the regression function when a covariate is mismeasured. The measurement error need not be classical. Employing the small measurement error approximation, we establish…