相关论文: Stable convergence of multiple Wiener-It\^{o} inte…

We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in terms of the underlying signal prior,…

The celebrated results of Koml\'os, Major and Tusn\'ady [Z. Wahrsch. Verw. Gebiete 32 (1975) 111-131; Z. Wahrsch. Verw. Gebiete 34 (1976) 33-58] give optimal Wiener approximation for the partial sums of i.i.d. random variables and provide a…

We construct a family $I_{n_{\eps}}(f)_{t}$ of continuous stochastic processes that converges in the sense of finite dimensional distributions to a multiple Wiener-It\^o integral $I_{n}^{H}(f1^{\otimes n}_{[0,t]})$ with respect to the…

With the use of tensor product of Hilbert space, and a diagonalization procedure from operator theory, we derive an approximation formula for a general class of stochastic integrals. Further we establish a generalized Fourier expansion for…

We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…

Models of self-organized criticality, which can be described as singular diffusions with or without (multiplicative) Wiener forcing term (as e.g. the Bak/Tang/Wiesenfeld- and Zhang-models), are analyzed. Existence and uniqueness of…

When applying Hamiltonian operator splitting methods for the time integration of multi-species Vlasov-Maxwell-Landau systems, the reliable and efficient numerical approximation of the Landau equation represents a fundamental component of…

We prove a scattering result near certain steady states for a Hartree equation for a random field. This equation describes the evolution of a system of infinitely many particles. It is an analogous formulation of the usual Hartree equation…

This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations with completely monotone kernels, such as linear…

We obtain explicit error bounds for the $d$-dimensional normal approximation on hyperrectangles for a random vector that has a Stein kernel, or admits an exchangeable pair coupling, or is a non-linear statistic of independent random…

For a continuous flow on a compact metric space, the aim of this paper is to prove a Conley-type decomposition of the strong chain recurrent set. We first discuss in details the main properties of strong chain recurrent sets. We then…

Fixed-point iterative sweeping methods were developed in the literature to efficiently solve steady state solutions of Hamilton-Jacobi equations and hyperbolic conservation laws. Similar as other fast sweeping schemes, the key components of…

Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this…

We extend almost everywhere convergence in Wiener-Wintner ergodic theorem for $\sigma$-finite measure to a generally stronger almost uniform convergence and present a larger, universal, space for which this convergence holds. We then extend…

Based on the convergence of their infinitesimal generators in the mixed topology, we provide a stability result for strongly continuous convex monotone semigroups on spaces of continuous functions. In contrast to previous results, we do not…

An analogue of the Stefan-Sussmann Theorem on manifolds with boundary is proven for normal distributions. These distributions contain vectors transverse to the boundary along its entirety. Plain integral manifolds are not enough to…

Modeling extreme-mass-ratio inspirals hinges on the accurate and efficient computation of gravitational-wave fluxes from generic Kerr orbits. Conventional frequency-domain techniques are often limited by costly auxiliary parameter searches…

In this work we study the estimation of the density of a totally positive random vector. Total positivity of the distribution of a random vector implies a strong form of positive dependence between its coordinates and, in particular, it…

We present a novel backward It{\^o}-Ventzell formula and an extension of the Aleeksev-Gr\"obner interpolating formula to stochastic flows. We also present some natural spectral conditions that yield direct and simple proofs of time uniform…

We propose to use L\'evy {\alpha}-stable distributions for constructing priors for Bayesian inverse problems. The construction is based on Markov fields with stable-distributed increments. Special cases include the Cauchy and Gaussian…