Related papers: Comparing Poisson and Gaussian channels (extended)
The accuracy of compound Poisson approximation to the sum $S=w_1S_1+w_2S_2+...+w_NS_N$ is estimated. Here $S_i$ are sums of independent or weakly dependent random variables, and $w_i$ denote weights. The overall smoothing effect of $S$ on…
The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by the accompanying compound Poisson laws and the estimates of the proximity of sequential…
In this article, we study the smallest distances between the zeros of Gaussian analytic functions over compact Riemann surfaces. Our main result is that, after appropriate rescaling, the point process of the smallest distances converge to a…
A continuous-time white Gaussian channel can be formulated using a white Gaussian noise, and a conventional way for examining such a channel is the sampling approach based on the classical Shannon-Nyquist sampling theorem, where the…
We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…
We present a method that allows, under suitable equivariance and regularity conditions, to determine the Poisson boundary of a diffusion starting from the Poisson boundary of a sub-diffusion of the original one. We then give two examples of…
Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…
This article compares the distributions of integer-valued random variables and Poisson random variables. It considers the total variation and the Wasserstein distance and provides, in particular, explicit bounds on the pointwise difference…
For a continuous-time additive white Gaussian noise (AWGN) channel with possible feedback, it has been shown that as sampling gets infinitesimally fine, the mutual information of the associative discrete-time channels converges to that of…
Several classical results on boundary crossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices,…
We consider a line network of nodes, connected by additive white Gaussian noise channels, equipped with local feedback. We study the velocity at which information spreads over this network. For transmission of a data packet, we give an…
Recently, Tian et al. [1] considered joint source-channel coding of transmitting a Gaussian source over $K$-user Gaussian broadcast channel, and derived an outer bound on the admissible distortion region. In [1], they stated "due to its…
We prove an exact relationship between the optimal denoising function and the data distribution in the case of additive Gaussian noise, showing that denoising implicitly models the structure of data allowing it to be exploited in the…
The transport phenomenon of active particles confined in 3D(three dimensional) corrugated confined channel with Gaussian noises is investigated. Large noise intensity perpendicular to the symmetry axis is good for the diffusion and current…
This paper is a step-by-step tutorial for fitting a mixture distribution to data. It merely assumes the reader has the background of calculus and linear algebra. Other required background is briefly reviewed before explaining the main…
We investigate Ussing's unidirectional fluxes and flux ratios of charged tracers motivated particularly by the insightful proposal of Hodgkin and Keynes on a relation between flux ratios and channel structure. Our study is based on analysis…
We prove limit theorems for functionals of a Poisson point process using the Malliavin calculus on the Poisson space. The target distribution is conditionally either a Gaussian vector or a Poisson random variable. The convergence is stable…
In this paper, we study two types of optical wireless channels under average-intensity constraints. One is called the Gaussian optical intensity channel, where the channel output models the converted electrical current corrupted by additive…
Suppose that a compound Poisson process is observed discretely in time and assume that its jump distribution is supported on the set of natural numbers. In this paper we propose a non-parametric Bayesian approach to estimate the intensity…
Motivated, in part, by the desire to develop an information-theoretic foundation for compound Poisson approximation limit theorems (analogous to the corresponding developments for the central limit theorem and for simple Poisson…