Related papers: Semidefinite Approximations of Invariant Measures …
We prove a complete characterization of the extremal invariant measures for half-space geometric last-passage percolation with an arbitrary boundary parameter. This is the first result of its kind for a model in the KPZ universality class…
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system…
This paper studies stochastic optimization problems with polynomials. We propose an optimization model with sample averages and perturbations. The Lasserre type Moment-SOS relaxations are used to solve the sample average optimization.…
The approximation of invariant measures for nonlinear ergodic stochastic differential equations (SDEs) is a central problem in scientific computing, with important applications in stochastic sampling, physics, and ecology. We first propose…
We study diffusion processes corresponding to infinite dimensional semilinear stochastic differential equations with local Lipschitz drift term and an arbitrary Lipschitz diffusion coefficient. We prove tightness and the Feller property of…
In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…
Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection,…
We develop a general framework for establishing non-uniqueness of stationary measures for stochastically forced dynamical systems possessing an almost surely invariant submanifold. Our main abstract result provides sufficient conditions for…
The standard moment-sum-of-squares (SOS) hierarchy is a powerful method for solving global polynomial optimization problems. However, its convergence relies on Putinar's Positivstellensatz, which requires the feasible set to satisfy the…
Consider a finite system of non-strict polynomial inequalities with solution set $S\subseteq\mathbb R^n$. Its Lasserre relaxation of degree $d$ is a certain natural linear matrix inequality in the original variables and one additional…
We investigate a class of moment problems, namely recovering a measure supported on the graph of a function from partial knowledge of its moments, as for instance in some problems of optimal transport or density estimation. We show that the…
Periodic point sets model all solid crystalline materials (crystals) whose atoms can be considered zero-sized points with or without atomic types. This paper addresses the fundamental problem of checking whether claimed crystals are novel,…
In this paper, we study a class of fractional semi-infinite polynomial programming problems involving s.o.s-convex polynomial functions. For such a problem, by a conic reformulation proposed in our previous work and the quadratic modules…
The article introduces a new algorithm for solving a class ofequilibrium problems involving strongly pseudomonotone bifunctions with Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with…
We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…
This paper introduces a new method to tackle the issue of the almost sure convergence of stochastic approximation algorithms defined from a differential inclusion. Under the assumption of slowly decaying step-sizes, we establish that the…
We consider the global minimization of a polynomial on a compact set B. We show that each step of the Moment-SOS hierarchy has a nice and simple interpretation that complements the usual one. Namely, it computes coefficients of a polynomial…
Every symbolic system supports a Borel measure that is invariant under the shift, but it is not known if every such systems supports a measure that is invariant under all of its automorphisms; known as a characteristic measure. We give…
We consider a piecewise smooth expanding map of the interval possessing two invariant subsets of positive Lebesgue measure and exactly two ergodic absolutely continuous invariant probability measures (ACIMs). When this system is perturbed…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…