Related papers: Trace formula for noise corrections to trace formu…
While convolutional sparse representations enjoy a number of useful properties, they have received limited attention for image reconstruction problems. The present paper compares the performance of block-based and convolutional sparse…
Sparse linear regression methods such as Lasso require a tuning parameter that depends on the noise variance, which is typically unknown and difficult to estimate in practice. In the presence of heavy-tailed noise or adversarial outliers,…
Reconstructing high derivatives of noisy measurements is an important step in many control, identification and diagnosis problems. In this paper, a heuristic is proposed to address this challenging issue. The framework is based on a…
We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently…
The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order…
This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…
We consider general (not necessarily Hamiltonian) perturbations of Hamiltonian systems with one degree of freedom near separatrices of the unperturbed system. We present asymptotic formulas for change of slow variables at evolution across…
The Langevin algorithm is a classic method for sampling from a given pdf in a real space. In its basic version, it only requires knowledge of the gradient of the log-density, also called the score function. However, in deep learning, it is…
We consider certain one dimensional ordinary stochastic differential equations driven by additive Brownian motion of variance $\varepsilon ^2$. When $\varepsilon =0$ such equations have an unstable non-hyperbolic fixed point and the drift…
A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can…
This paper deals with the numerical approximation of semilinear parabolic stochastic partial differential equation (SPDE) driven simultaneously by Gaussian noise and Poisson random measure, more realistic in modeling real world phenomena.…
In the recent literature one can find calculations of various one--loop amplitudes, like anomalies, tadpoles and vacuum energies, on specific types of orbifolds, like S^1/Z_2. This work aims to give a general description of such one--loop…
In many real-world applications, optimization problems evolve continuously over time and are often subject to stochastic noise. We consider a stochastic time-varying optimization problem in which the objective function $f(x;t)$ changes…
A one-step analysis of Anderson acceleration with general algorithmic depths is presented. The resulting residual bounds within both contractive and noncontractive settings reveal the balance between the contributions from the higher and…
We prove a large deviation principle result for solutions of abstract stochastic evolution equations perturbed by small Levy noise. We use general large deviations theorems of Varadhan and Bryc, viscosity solutions of integro-partial…
We address a parametric joint detection-estimation problem for discrete signals of the form $x(t) = \sum_{n=1}^{N} \alpha_n e^{-i \lambda_n t } + \epsilon_t$, $t \in \mathbb{N}$, with an additive noise represented by independent centered…
In this paper, we present a novel semi-implicit numerical scheme for the stochastic Cahn--Hilliard equation driven by multiplicative noise. By reformulating the original equation into an equivalent stochastic scalar auxiliary variable…
We obtain a new simple formula for the regularized traces of singular ordinary differential operators.
In this study, we investigate the traces and solutions of inverse nodal problems of discontinuous Sturm-Liouville operators with retarded argument and with a finite number of transmission conditions.
Informed by recent work on tensor singular value decomposition and circulant algebra matrices, this paper presents a new theoretical bridge that unifies the hypercomplex and tensor-based approaches to singular value decomposition and robust…