相关论文: Approximating Shepp's constants for the Slepian pr…

Quasi-periodicity refers to a pattern in a function where it appears periodic but has evolving amplitudes over time. This is often the case in practical settings such as the modeling of case counts of infectious disease or the carbon…

We study the convergence rate for the last iterate of stochastic gradient descent (SGD) and stochastic heavy ball (SHB) in the parametric setting when the objective function $F$ is globally convex or non-convex whose gradient is…

Sequential Quadratic Programming (SQP) is a powerful class of algorithms for solving nonlinear optimization problems. Local convergence of SQP algorithms is guaranteed when the Hessian approximation used in each Quadratic Programming…

This contribution establishes exact tail asymptotics of $\sup_{(s,t)\in\mathbf{E}}$ $X(s,t)$ for a large class of nonhomogeneous Gaussian random fields $X$ on a bounded convex set $\mathbf{E}\subset\mathbb{R}^2$, with variance function that…

Recent years have seen an increasing use of Signal Temporal Logic (STL) as a formal specification language for symbolic control, due to its expressiveness and closeness to natural language. Furthermore, STL specifications can be encoded as…

This SSFG Lp stability theorem can predict permissible forcing amplitudes below which a finite nonlinear input-output gain can be maintained. Our analysis employs Linear Matrix Inequalities (LMI) and Sum-of-Squares (SOS) as the primary…

We study approximation properties of linear sampling operators in the spaces $L_p$ for $1\le p<\infty$. By means of the Steklov averages, we introduce a new measure of smoothness that simultaneously contains information on the smoothness of…

Stochastic approximation (SA) is a classical approach for stochastic convex optimization. Previous studies have demonstrated that the convergence rate of SA can be improved by introducing either smoothness or strong convexity condition. In…

We study a variety of stochastic contact processes -- directly related to models of rumor and disease spreading -- from the viewpoint of their constants of motion, either exact or approximated. Much as in deterministic systems, constants of…

Smoothed Particle Hydrodynamics (SPH_ is a mesh-free Lagrangian method renowned for modeling large deformations and free-surface flows, yet classical formulations remain confined to deterministic systems. We introduce Stochastic SPH…

We consider stochastic processes $Y(t)$ which can be represented as $Y(t)=(X(t))^s, s \in \mathbb{N},$ where $X(t)$ is a stationary strictly sub-Gaussian process and build a wavelet-based model that simulates $Y(t)$ with given accuracy and…

The Quantum Symmetric Simple Exclusion Process (Q-SSEP) is a model for quantum stochastic dynamics of fermions hopping along the edges of a graph with Brownian noisy amplitudes and driven out-of-equilibrium by injection-extraction processes…

In this contribution we discuss the relation between Pickands-type constants defined for certain Brown-Resnick stationary process $W(t),t\in R$ as $$\mathcal{H}_W^\delta= \lim_{T\to\infty} T^{-1} E{ \left(\sup_{t\in \delta Z \cap [0,T]}…

Let $A = -{\rm div} \,a(\cdot) \nabla$ be a second order divergence form elliptic operator on $\R^n$ with bounded measurable real-valued coefficients and let $W$ be a cylindrical Brownian motion in a Hilbert space $H$. Our main result…

The goal of this paper is to study the behavior of certain solutions to the Swift-Hohenberg equation on a one-dimensional torus $\mathbb{T}$. Combining results from $\Gamma$-convergence and ODE theory, it is shown that solutions…

We obtain an optimal bound for a Gaussian approximation of a large class of vector-valued random processes. Our results provide a substantial generalization of earlier results that assume independence and/or stationarity. Based on the decay…

Normal comparison lemma and Slepian's inequality are essential tools in the study of Gaussian processes. In this paper we extend normal comparison lemma and derive various related comparison inequalities including Slepian's inequality for…

We consider two steady-state heat conduction systems called, $S$ and $S_\alpha$, in a multidimensional bounded domain $D$ for the Poisson equation with source energy $g$. In one system, we impose mixed boundary conditions (temperature $b$…

Observed efficiencies of industrial power plants are often approximated by the square-root formula: $1-\sqrt{T_-/T_+}$, where $T_+ (T_-)$ is the highest (lowest) temperature achieved in the plant. This expression can be derived within…

Soft extrapolation refers to the problem of recovering a function from its samples, multiplied by a fast-decaying window and perturbed by an additive noise, over an interval which is potentially larger than the essential support of the…