Related papers: Relaxed sector condition
In this paper, we study the restricted isometry property of partial random circulant matrices. For a bounded subgaussian generator with independent entries, we prove that the partial random circulant matrices satisfy $s$-order RIP with high…
In this note we present some generalized versions of the Krein-Rutman theorem for sectorial operators. They are formulated in a fashion that can be easily applied to elliptic operators. Another feature of these generalized versions is that…
In this note, we prove a conditionally centered version of the quenched weak invariance principle under the Hannan condition, for stationary processes. In the course, we obtain a (new) construction of the fact that any stationary process…
The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…
We study the convergence of variationally regularized solutions to linear ill-posed operator equations in Banach spaces as the noise in the right hand side tends to $0$. The rate of this convergence is determined by abstract smoothness…
In this paper, we are concerned with stationarity conditions and qualification conditions for optimization problems with disjunctive constraints. This class covers, among others, optimization problems with complementarity, vanishing, or…
In this paper we study the central limit theorem for additive functionals of stationary Markov chains with general state space by using a new idea involving conditioning with respect to both the past and future of the chain. Practically, we…
New form of sufficient optimality condition is obtained in comparison with the Mangasarian sufficiency theorem. Both finite and infinite values of objective functional are allowed since concepts of overtaking and weakly overtaking…
Motivated by random evolutions which do not start from equilibrium, in a recent work, Peligrad and Voln\'{y} (2018) showed that the quenched CLT (central limit theorem) holds for ortho-martingale random fields. In this paper, we study the…
A version of Gabor expansion over a lattice of critical density is shown to converge to an arbitrary function that belongs to domain of the oscillator operator. This expansion is used for approximation of an arbitrary function concentrated…
A sufficient condition for the stability of a system resulting from the interconnection of dynamical systems is given by the small gain theorem. Roughly speaking, to apply this theorem, it is required that the gains composition is…
We consider the Moment-SOS hierarchy in polynomial optimization. We first provide a sufficient condition to solve the truncated K-moment problem associated with a given degree-$2n$ pseudo-moment sequence $\phi$ n and a semi-algebraic set $K…
We prove a uniqueness result of the unbounded solution for a quadratic backward stochastic differential equation whose terminal condition is unbounded and whose generator $g$ may be non-Lipschitz continuous in the state variable $y$,…
The convergence behavior of gradient methods for minimizing convex differentiable functions is one of the core questions in convex optimization. This paper shows that their well-known complexities can be achieved under conditions weaker…
We establish a sufficient condition for the tightness of a sequence of stochastic processes. Our condition makes it possible to study processes with accumulations of fixed times of discontinuity. Our motivation comes from the study of…
In this paper, we establish a spatial central limit theorem for a large class of supercritical branching, not necessarily symmetric, Markov processes with spatially dependent branching mechanisms satisfying a second moment condition. This…
We show stability and locality of the minimal supersolution of a forward backward stochastic differential equation with respect to the underlying forward process under weak assumptions on the generator. The forward process appears both in…
In this paper, we study the problem of \textit{constrained} and \textit{stochastic} continuous submodular maximization. Even though the objective function is not concave (nor convex) and is defined in terms of an expectation, we develop a…
When the limiting compensator of a sequence of martingales is continuous, we obtain a weak convergence theorem for the martingales; the limiting process can be written as a Brownian motion evaluated at the compensator and we find sufficient…
Extreme-value theory for random vectors and stochastic processes with continuous trajectories is usually formulated for random objects all of whose univariate marginal distributions are identical. In the spirit of Sklar's theorem from…