Related papers: Gamma Noise Analysis
In this paper, we propose a quantized learning equation with a monotone increasing resolution of quantization and stochastic analysis for the proposed algorithm. According to the white noise hypothesis for the quantization error with dense…
The objective of the paper is to identify and investigate all possible types of asymptotic behavior for the maximum likelihood estimators of the unknown parameters in the second-order linear stochastic ordinary differential equation driven…
This paper studies the linear stochastic partial differential equation of fractional orders both in time and space variables $\left(\partial^\beta + \frac{\nu}{2} (-\Delta)^{\alpha/2} \right) u(t,x)= \lambda u(t,x) \dot{W}(t,x)$, where…
This article studies (optimal) $W^{2m-1,\infty}$-regularity for the polyharmonic equation $(-\Delta)^m u = Q \; \mathcal{H}^{n-1} \llcorner \Gamma$, where $\Gamma$ is a (suitably regular) $(n-1)$-dimensional submanifold of $\mathbb{R}^n$,…
In this paper, we study the quantization errors of modulo sigma-delta modulated finite, asymptotically-infinite, infinite causal stable ARMA processes. We prove that the normalized quantization error can be taken as a uniformly distributed…
We investigate and compare the fundamental performance of several distributed learning methods that have been proposed recently. We do this in the context of a distributed version of the classical signal-in-Gaussian-white-noise model, which…
This article provides a general expression for infinitely divisible multivariate gamma distributions defined by their Laplace transforms, as well as the conditional Laplace transform of infinitely divisible multivariate gamma…
We consider an infinite-dimensional dynamical system with polynomial nonlinearity and additive noise given by a finite number of Wiener processes. By studying how randomness is spread by the system we develop a counterpart of Hormander's…
The classical phase retrieval problem arises in contexts ranging from speech recognition to x-ray crystallography and quantum state tomography. The generalization to matrix frames is natural in the sense that it corresponds to quantum…
We give a general approach to infinite dimensional non-Gaussian Analysis for measures which need not have a logarithmic derivative. This framework also includes the possibility to handle measures of Poisson type.
In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian)…
We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…
A fully diagonalized spectral method using generalized Laguerre functions is proposed and analyzed for solving elliptic equations on the half line. We first define the generalized Laguerre functions which are complete and mutually…
This paper is concerned with an inverse random source problem for the one-dimensional stochastic Helmholtz equation with attenuation. The source is assumed to be a microlocally isotropic Gaussian random field with its covariance operator…
The gamma difference distribution is defined as the difference of two gamma distributions, with in general different shape and rate parameters. Starting with knowledge of the corresponding characteristic function, a second order linear…
We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of…
This paper studies the rich dynamics of one-dimensional granular media equations with attractive quadratic interactions. Building on the monotone dynamical systems framework developed in an earlier work, we allow for multiplicative noise,…
In this article, we improve the Strichartz estimates obtained in [12] for the Schr\"odinger equation with white noise dispersion in one dimension. This allows us to prove global well posedness when a quintic critical nonlinearity is added…
White noise is a fundamental and fairly well understood stochastic process that conforms the conceptual basis for many other processes, as well as for the modeling of time series. Here we push a fresh perspective toward white noise that,…
In this paper, we analyze Galerkin approximations for stochastic evolution equations driven by an additive Gaussian noise which is temporally white and spatially fractional with Hurst index less than or equal to $1/2$. First we regularize…