Related papers: Local convergence near equilibria for distribution…
We analyze two variants of Local Gradient Descent applied to distributed logistic regression with heterogeneous, separable data and show convergence at the rate $O(1/KR)$ for $K$ local steps and sufficiently large $R$ communication rounds.…
An averaging result is proved for stochastic evolution equations with highly oscillating coefficients. This result applies in particular to equations with almost periodic coefficients. The convergence to the solution of the averaged…
Consider a sequence $P_n$ of positive recurrent transition matrices or kernels that approximate a limiting infinite state matrix or kernel $P_{\infty}$. Such approximations arise naturally when one truncates an infinite state Markov chain…
We study the effective approximation for a nonlocal stochastic Schrodinger equation with a rapidly oscillating, periodically time-dependent potential. We use the natural diffusive scaling of heterogeneous system and study the limit…
In this article we introduce several kinds of easily implementable explicit schemes, which are amenable to Khasminski's techniques and are particularly suitable for highly nonlinear stochastic differential equations (SDEs). We show that…
This work studies how the choice of the representation for parametric, spatially distributed inputs to elliptic partial differential equations (PDEs) affects the efficiency of a polynomial surrogate, based on Taylor expansion, for the…
The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to…
This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The…
Bounds on convergence rate to the invariant distribution for a class of stochastic differential equations (SDEs) with a gradient-type drift are obtained.
In the present article, we discuss some aspects of the local stability analysis for a class of abstract functional differential equations. This is done under smoothness assumptions which are often satisfied in the presence of a…
We study the local convergence of diffusive mean-field systems, including Wasserstein gradient flows, min-max dynamics, and multi-species games. We establish exponential local convergence in $\chi^2$-divergence with sharp rates, under two…
This paper investigates the tilt stability of local minimizers for nonlinear programs under the relaxed constant rank constraint qualification in finite dimensions. By employing a neighborhood primal-dual approach and extending calculus…
Gradient descent and stochastic gradient descent are central to modern machine learning, yet their behavior under large step sizes remains theoretically unclear. Recent work suggests that acceleration often arises near the edge of…
A powerful tool for studying long-term convergence of a Markov process to its stationary distribution is a Lyapunov function. In some sense, this is a substitute for eigenfunctions. For a stochastically ordered Markov process on the…
Distributed linear algebraic equation over networks, where nodes hold a part of problem data and cooperatively solve the equation via node-to-node communications, is a basic distributed computation task receiving an increasing research…
This paper examines the local linear regression (LLR) estimate of the conditional distribution function $F(y|x)$. We derive three uniform convergence results: the uniform bias expansion, the uniform convergence rate, and the uniform…
We describe and analyse Levenberg-Marquardt methods for solving systems of nonlinear equations. More specifically, we propose an adaptive formula for the Levenberg-Marquardt parameter and analyse the local convergence of the method under…
Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper, we provide…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
In this paper we investigate explicit numerical approximations for stochastic differential delay equations (SDDEs) under a local Lipschitz condition by employing the adaptive Euler-Maruyama (EM) method. Working in both finite and infinite…