Related papers: Asymptotic analysis of extended two-dimensional na…
We provide an asymptotic analysis of linear transport problems in the diffusion limit under minimal regularity assumptions on the domain, the coefficients, and the data. The weak form of the limit equation is derived and the convergence of…
We prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected quadratic transportation cost for empirical measures of two samples of independent…
This paper develops a general asymptotic theory of local polynomial (LP) regression for spatial data observed at irregularly spaced locations in a sampling region $R_n \subset \mathbb{R}^d$. We adopt a stochastic sampling design that can…
A non-local dynamic homogenization technique for the analysis of a viscoelastic heterogeneous material which displays a periodic microstructure is herein proposed. The asymptotic expansion of the micro-displacement field in the transformed…
When using the boundary integral equation method to solve a boundary value problem, the evaluation of the solution near the boundary is challenging to compute because the layer potentials that represent the solution are nearly-singular…
We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target…
Much work in the study of large deviations for random graph models is focused on the dense regime where the theory of graphons has emerged as a principal tool. These tools do not give a good approach to large deviation problems for random…
We investigate the statistics of encounters of a diffusing particle with different subsets of the boundary of a confining domain. The encounters with each subset are characterized by the boundary local time on that subset. We extend a…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
We develop a principled way of identifying probability distributions whose independent and identically distributed (iid) realizations are compressible, i.e., can be well-approximated as sparse. We focus on Gaussian random underdetermined…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…
This paper proposes a widely applicable method of approximate maximum-likelihood estimation for multivariate diffusion process from discretely sampled data. A closed-form asymptotic expansion for transition density is proposed and…
This thesis is concerned with the asymptotic behavior of solutions of stochastic $p$-Laplace equations driven by non-autonomous forcing on $\mathbb{R}^n$. Two cases are studied, with additive and multiplicative noise respectively. Estimates…
We study the probability densities of finite-time or \local Lyapunov exponents (LLEs) in low-dimensional chaotic systems. While the multifractal formalism describes how these densities behave in the asymptotic or long-time limit, there are…
We propose a new method for obtaining complete asymptotic expansions in a systematic manner, which is suitable for counting sequences of various graph families in dense regime. The core idea is to encode the two-dimensional array of…
The spatial extension and complexity of the eigenfunctions of an open finite-size two-dimensional (2D) random system are systematically studied for a random collection of systems ranging from weakly scattering to localized. The…
Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…
This paper concerns the asymptotic expansion of the solution of the Dirichlet-Laplace problem in a domain with small inclusions. This problem is well understood for the Neumann condition in dimension greater than two or Dirichlet condition…
Motivated by practical applications in heat conduction and contaminant transport, we consider heat and mass diffusion across a perturbed interface separating two finite regions of distinct diffusivity. Under the assumption of continuity of…
We present expressions for the coefficients which arise in asymptotic expansions of multiple integrals of Laplace type (the first term of which is known as Laplace's approximation) in terms of asymptotic series of the functions in the…