Related papers: Minimax probabilities for Aubry-Mather Problems
We solve explicitly a certain minimization problem for probability measures in one dimension involving an interaction energy that arises in the modelling of aggregation phenomena. We show that in a certain regime minimizers are absolutely…
This paper concerns the study of a broad class of minimal time functions corresponding to control problems with constant convex dynamics and closed target sets in arbitrary Banach spaces. In contrast to other publications, we do not impose…
A variety of physical phenomena involve the nonlinear transfer of energy from weakly damped modes subjected to external forcing to other modes which are more heavily damped. In this work we explore this in (finite-dimensional) stochastic…
A class of causal variational principles on a compact manifold is introduced and analyzed both numerically and analytically. It is proved under general assumptions that the support of a minimizing measure is either completely timelike, or…
The main objective of this work is to study the existence of Lagrange multipliers for infinite dimensional problems under G\^ateux differentiability assumptions on the data. Our investigation follows two main steps: the proof of the…
We focus on one-sided, mixture-based stopping rules for the problem of sequential testing a simple null hypothesis against a composite alternative. For the latter, we consider two cases---either a discrete alternative or a continuous…
We study existence of probability measure valued jump-diffusions described by martingale problems. We develop a simple device that allows us to embed Wasserstein spaces and other similar spaces of probability measures into locally compact…
This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…
In this work, optimality conditions and classical results from duality theory are derived for continuous-time linear optimization problems with inequality constraints. The optimality conditions are given in the Karush-Kuhn-Tucker form. Weak…
Minimal thinness is a notion that describes the smallness of a set at a boundary point. In this paper, we provide tests for minimal thinness at finite and infinite minimal Martin boundary points for a large class of purely discontinuous…
We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or…
We study well posedness of time--dependent Hamilton--Jacobi equations on a network, coupled with a continuous initial datum and a flux limiter. We show existence and uniqueness of solutions as well as stability properties. The novelty of…
This paper is concerned with the study of Aubry-Mather and weak KAM theories for contact Hamiltonian systems with Hamiltonians $H(x,u,p)$ defined on $T^*M\times\mathbb{R}$, satisfying Tonelli conditions with respect to $p$ and…
We propose matrix commutator based stability characterization for discrete-time switched linear systems under restricted switching. Given an admissible minimum dwell time, we identify sufficient conditions on subsystems such that a switched…
Let $X$ be a locally compact Polish space. A random measure on $X$ is a probability measure on the space of all (nonnegative) Radon measures on $X$. Denote by $\mathbb K(X)$ the cone of all Radon measures $\eta$ on $X$ which are of the form…
This paper firstly presents the necessary and sufficient conditions for a kind of discrete-time robust stochastic optimal control problem with convex control domains. As it is an "inf sup problem", the classical variational method is…
We study existence of minimisers to the least gradient problem on a strictly convex domain in two settings. On a bounded domain, we allow the boundary data to be discontinuous and prove existence of minimisers in terms of the Hausdorff…
Obtaining sharp estimates for quantities involved in a given model is an integral part of the modeling process. For dynamical systems whose orbits display a complicated, perhaps chaotic, behaviour, the aim is usually to estimate time or…