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In the objective of studying concentration and oscillation properties of eigenfunctions of the discrete Laplacian on regular graphs, we construct a pseudo-differential calculus on homogeneous trees, their universal covers. We define symbol…

A compound Poisson process whose jump measure and intensity are unknown is observed at finitely many equispaced times. We construct a purely data-driven estimator of the L\'evy density $\nu$ through the spectral approach using general…

The Dominative $p$-Laplacian is the operator defined for $2\le p < \infty$ as follows: \begin{equation}\label{dominativep} \mathcal{L}_{p}u(x)=\frac{1}{p}\left(\lambda_{1}+\ldots+\lambda_{N-1}\right)+\frac{(p-1)}{p}\lambda_{N},…

We focus on the estimation of the intensity of a Poisson process in the presence of a uniform noise. We propose a kernel-based procedure fully calibrated in theory and practice. We show that our adaptive estimator is optimal from the oracle…

We establish Poisson and compound Poisson approximations for stabilizing statistics of $\beta$-mixing point processes and give explicit rates of convergence. Our findings are based on a general estimate of the total variation distance of a…

We study the problem of non-parametric Bayesian estimation of the intensity function of a Poisson point process. The observations are $n$ independent realisations of a Poisson point process on the interval $[0,T]$. We propose two related…

We propose a perturbative approach to determine the time-dependent Dyson map and the metric operator associated with time-dependent non-Hermitian Hamiltonians. We apply the method to a pair of explicitly time-dependent two dimensional…

This paper considers the problem of approximating the inverse of the wave-equation Hessian, also called normal operator, in seismology and other types of wave-based imaging. An expansion scheme for the pseudodifferential symbol of the…

The study of dispersive properties of Schr\"odinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be…

We consider random transformations $T_\omega^n:=T_{\sigma^{n-1}\omega}\circ\cdots\circ T_{\sigma\omega}\circ T_\omega,$ where each map $T_{\omega}$ acts on a complete metrizable space $M$. The randomness comes from an invertible ergodic…

We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and…

We study the connections existing between max-infinitely divisible distributions and Poisson processes from the point of view of functional analysis. More precisely, we derive functional identities for the former by using well-known results…

We consider the semiclassical operator $\hat{H}(\epsilon,h):=H_{0}(hD_{x})+\epsilon \tilde{P}_{0}$ on $L^{2}(\mathbb{R}^{l})$, where the symbol of $\hat{H}(\epsilon,h)$ corresponds to a perturbed classical Hamiltonian of the form:…

We consider a finite region of a d-dimensional lattice of nonlinear Hamiltonian rotators, where neighbouring rotators have opposite spins and are coupled by a small potential of order $\varepsilon^a,\, a\geq1/2$. We weakly stochastically…

We consider second order uniformly elliptic operators of divergence form in $\R^{d+1}$ whose coefficients are independent of one variable. Under the Lipschitz condition on the coefficients we characterize the domain of the Poisson operators…

The main result of this paper is a convexity theorem for momentum mappings of certain hamiltonian actions of noncompact semisimple Lie groups. The image is required to fall within a certain open subset D of the (dual of the) Lie algebra,…

Let A(x) be a holomorphic family of bounded self-adjoint operators on a separable Hilbert space H and let A(x)_n be the orthogonal compressions of A(x) to the span of first n elements of an orthonormal basis of H. The problem considered…

In this article, we study the problem of parameter estimation for a discrete Ornstein - Uhlenbeck model driven by Poisson fractional noise. Based on random walk approximation for the noise, we study least squares and maximum likelihood…

Let $\Phi$ be a real valued function of one real variable, let $L$ denote an elliptic second order formally self-adjoint differential operator with bounded measurable coefficients, and let $P$ stand for the Poisson operator for $L$. A…

We study the spectrum of the Robin Laplacian with a complex Robin parameter $\alpha$ on a bounded Lipschitz domain $\Omega$. We start by establishing a number of properties of the corresponding operator, such as generation properties, local…