Related papers: A functional limit theorem for general shot noise …
We study some fundamental properties, such as the transience, the recurrence, the first passage times and the zero-set of a certain type of sawtooth Markov processes, called extremal shot noise processes. The sets of zeros of the latter are…
In the context of non-Gaussian analysis, Schneider [27] introduced grey noise measures, built upon Mittag-Leffler functions; analogously, grey Brownian motion and its generalizations were constructed (see, for example, [25], [6], [7], [8]).…
Our principal aim is to observe the Markov discrete-time process of population growth with long-living trajectory. First we study asymptotical decay of generating function of Galton-Watson process for all cases as the Basic Lemma.…
We derive a functional limit theorem for the partial maxima process based on a long memory stationary $\alpha$-stable process. The length of memory in the stable process is parameterized by a certain ergodic-theoretical parameter in an…
We propose a derivation of the full counting statistics of electronic current based on a positive-operator-valued measure. Our approach justifies the Levitov-Lesovik formula in the long-time limit, but can be generalized to the detection of…
Through certain appropriate constructions, we establish periodic solutions in distribution for some stochastic differential equations with infinite-dimensional Levy noise. Additionally, we obtain the corresponding periodic measures and…
Consider the following local empirical process indexed by $K\in \mathcal{G}$, for fixed $h>0$ and $z\in \mathbb{R}^d$: $$G_n(K,h,z):=\sum_{i=1}^n K \Bigl(\frac{Z_i-z}{h^{1/d}}\Big) - \mathbbE \Bigl(K \Bigl(\frac{Z_i-z}{h^{1/d}}\Big)\Big),$$…
With the use of Hida's white noise space theory space theory and spaces of stochastic distributions, we present a detailed analytic continuation theory for classes of Gaussian processes, with focus here on Brownian motion. For the latter,…
We study the work fluctuations of a particle, confined to a moving harmonic potential, under the influence of friction and external Poissonian shot noise. The asymmetry of the noise induces an effective nonlinearity in the potential, which…
We consider a system of diffusing particles on the real line in a quadratic external potential and with repulsive electrostatic interaction. The empirical measure process is known to converge weakly to a deterministic measure-valued process…
Powerful approaches to squeeze the motional state of a harmonic oscillator rely on the stepwise modulation of its resonance frequency. Such protocols can be limited by forces that vary slowly between experimental runs but are constant…
The generalization of fractional Brownian motion in infinite-dimensional white and grey noise spaces has been recently carried over, following the Mandelbrot-Van Ness representation, through Riemann-Liouville type fractional operators. Our…
This paper presents uniform-in-time finite-sample bounds for regularized linear regression with vector-valued outputs and conditionally zero-mean subgaussian noise. By revisiting classical self-normalized martingale arguments, we obtain…
A self-consistent theory of shot noise in ballistic two-terminal conductors under the action of long-range Coulomb correlations is presented. Analytical formulas for the electron distribution function and its fluctuation along the…
We consider, for a diffusion process in R^n, the Gallavotti-Cohen functional, defined as the empirical power dissipated in a time interval by the non-conservative part of the drift. We prove a large deviation principle in the limit in which…
Hawkes process is a self-exciting point process with clustering effect whose intensity depends on its entire past history. It has wide applications in neuroscience, finance and many other fields. In this paper, we obtain a functional…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
We give a general Gaussian bound for the first chaos (or innovation) of point processes with stochastic intensity constructed by embedding in a bivariate Poisson process. We apply the general result to nonlinear Hawkes processes, providing…
We study the fundamental limits of noise spectroscopy using estimation theory, Faraday rotation probing of an atomic spin system, and squeezed light. We find a simple and general expression for the Fisher information, which quantifies the…
In this article, we study fluctuations of the volume of a stable sausage defined via a $d$-dimensional rotationally invariant $\alpha$-stable process. As the main results, we establish a functional central limit theorem (in the case when…