相关论文: Correlation based passive imaging with a white noi…

The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements,…

Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…

On the basis of the competing cubic-quintic nonlinearity model, stability (instability) of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the…

This paper investigates the inverse scattering problem of recovering a sound-soft obstacle using passive measurements taken from randomly distributed point sources. The randomness introduced by these sources poses significant challenges,…

This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…

The cosmological stochastic gravitational-wave background produced by the mildly non-linear evolution of density fluctuations is analyzed, in the frame of an Einstein-de Sitter model, by means of a fully relativistic perturbation expansion…

We investigate the quantization of a single unstable mode in a real scalar field subject to a Robin boundary condition in (1+1)-dimensional half-Minkowski spacetime. The instability arises from an imaginary frequency mode - analogous to…

This paper studies the behaviour of quadratic variations of a stochastic wave equation driven by a noise that is white in space and fractional in time. Complementing the analysis of quadratic variations in the space component carried out by…

This paper is concerned with the long-time dynamics of the nonlinear wave equation in one-space dimension, $$ u_{tt} - \delta^2 u_{xx} +V'(u) =0 \qquad x\in [0,1] $$ where $\delta>0$ is a parameter and $V(u)$ is a potential bounded from…

Gravitational-wave echoes in the post-merger ringdown phase are under intense scrutiny as probes of near-horizon quantum structures and as signatures of exotic states of matter in ultracompact stars. We present an analytical template that…

We consider problem of signal detection in Gaussian white noise. Test statistics are linear combinations of squares of estimators of Fourier coefficients or $\mathbb{L}_2$-norms of kernel estimators. We point out necessary and sufficient…

Estimating the rate of convergence of the empirical measure of an i.i.d. sample to the reference measure is a classical problem in probability theory. Extending recent results of Ambrosio, Stra and Trevisan on 2-dimensional manifolds, in…

Consider the stochastic heat equation $\partial_tu=\mathscr{L}u+\lambda\sigma(u)\xi$, where $\mathscr{L}$ denotes the generator of a L\'{e}vy process on a locally compact Hausdorff Abelian group $G$, $\sigma:\mathbf{R}\to\mathbf{R}$ is…

In Gel'fand's inverse problem, one aims to determine the topology, differential structure and Riemannian metric of a compact manifold $M$ with boundary from the knowledge of the boundary $\partial M,$ the Neumann eigenvalues $\lambda_j$ and…

This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary gaussian noise having unknown correlation function. A general model selection procedure on the basis of…

In this article, we consider the stochastic wave equation in spatial dimension $d=1$, with linear term $\sigma(u)=u$ multiplying the noise. This equation is driven by a Gaussian noise which is white in time and fractional in space with…

In this paper the reflection and transmission of waves by a three-dimensional random medium are studied in a white-noise and paraxial regime. The limit system derives from the acoustic wave equations and is described by a coupled system of…

In this paper, we introduce a novel, data-driven approach for solving high-dimensional Bayesian inverse problems based on partial differential equations (PDEs), called Weak Neural Variational Inference (WNVI). The method complements real…

Motivated by applications to wireless communications, this paper addresses the propagation of waves transmitted by ambient noise sources and interacting with metamaterials. We discuss a generalized Helmholtz-Kirchhoff identity that is valid…

After the first direct detection of gravitational waves (GW), detection of stochastic background of GWs is an important next step, and the first GW event suggests that it is within the reach of the second-generation ground-based GW…