Related papers: A functional limit theorem for general shot noise …

We present two linear relations between an arbitrary (real tempered second order) generalized stochastic process over $\mathbb{R}^{d}$ and White Noise processes over $\mathbb{R}^{d}$. The first is that any generalized stochastic process can…

We examine the statistics of current fluctuations in a junction with a quantum dot described by Kondo Hamiltonian. With the help of Keldysh technique we calculate shot noise as a function of applied voltage at zero temperature using the…

Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform…

Let $\xi_i$, $i\in \mathbb {N}$, be independent copies of a L\'{e}vy process $\{\xi(t),t\geq0\}$. Motivated by the results obtained previously in the context of the random energy model, we prove functional limit theorems for the process…

When collections of functional data are too large to be exhaustively observed, survey sampling techniques provide an effective way to estimate global quantities such as the population mean function. Assuming functional data are collected…

Quantitative limit theorems for non-linear functionals on the Wiener space are considered. Given the possibly infinite sequence of kernels of the chaos decomposition of such a functional, an estimate for different probability distances…

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to L{\'e}vy processes in the Skorokhod space…

By a random process with immigration at random times we mean a shot noise process with a random response function (response process) in which shots occur at arbitrary random times. The so defined random processes generalize random processes…

A common assumption in signal processing is that underlying data numerically conforms to a Gaussian distribution. It is commonly utilized in signal processing to describe unknown additive noise in a system and is often justified by citing…

Typical properties of computing circuits composed of noisy logical gates are studied using the statistical physics methodology. A growth model that gives rise to typical random Boolean functions is mapped onto a layered Ising spin system,…

This article studies the scaling limit of a class of shot-noise fields defined on an independently marked stationary Poisson point process and with a power law response function. Under appropriate conditions, it is shown that the shot-noise…

Quantum error correction is essential for robust quantum information processing with noisy devices. As bosonic quantum systems play a crucial role in quantum sensing, communication, and computation, it is important to design error…

We obtain the empirical strong law of large numbers, empirical Glivenko-Cantelli theorem, central limit theorem, functional central limit theorem for various nonparametric Bayesian priors which include the Dirichlet process with general…

When the rate of shot noise is controlled by on-off states we speak of intermittent shot noise. The on-off states lead to alternately occurring clusters of events and intermissions, respectively. We derive the power spectrum of the…

We observe that given two (compatible) classes of functions $\mathcal{F}$ and $\mathcal{H}$ with small capacity as measured by their uniform covering numbers, the capacity of the composition class $\mathcal{H} \circ \mathcal{F}$ can become…

Recently, the so-called next-generation neural mass models have received a lot of attention of the researchers in the field of mathematical neuroscience. The ability of these models to account for the degree of synchrony in neural…

The following random recurrency: $$ W_{n+1} = U_{n+1} ( W_n + \Lambda_{n+1} ) $$ where $W_{-1}=0.$ is known to be associated with the shot noise : $$ W_{t} = \sum_{0<t_k<t} \Lambda_{k} e^{-(t-t_k)} $$ where the $t_k$ are the dates of a…

Using the 'drift-diffusion-Langevin' equation we show that, at least in one geometry, finite-frequency shot noise is of the order of the 'full' shot noise $2eI$ provided the sample is either short or long enough, $L > L_0(\omega)$. Here…

We prove a central limit type theorem for critical marked Hawkes processes. We study the case where the marks are i.i.d. with nonnegative values and their common distribution is either heavy tailed or has finite variance. The kernel…

We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in $\mathbb{R}^d$. The dynamics we study here are those of a Markov birth-death process. We prove functional limit…