相关论文: Harness processes and harmonic crystals

We present a microscopic theory of cross-correlated noise processes, starting from a Hamiltonian system-reservoir description. In the proposed model, the system is nonlinearly coupled to a reservoir composed of harmonic oscillators, which…

L\'evy stochastic processes, with noise distributed according to a L\'evy stable distribution, are ubiquitous in science. Focusing on the case of a particle trapped in an external harmonic potential, we address the problem of finding…

We provide asymptotic results and develop high frequency statistical procedures for time-changed L\'evy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with…

This paper investigates the asymptotic behavior of suitably time-modulated Hawkes processes with heavy-tailed kernels in a nearly unstable regime. We show that, under appropriate scaling, both the intensity processes and the rescaled Hawkes…

We studied the statistical properties of the HI-to-H$_2$ transition observed in absorption in the local diffuse and multiphase ISM to identify the physical processes controlling the probability of occurrence of any line of sight. The…

Let $(X,d)$ be a locally compact separable ultrametric space. Given a measure $m$ on $X$ and a function $C$ defined on the set $\mathcal{B}$ of all balls $B\subset X$ we consider the hierarchical Laplacian $L=L_{C}$. The operator $L$ acts…

In this paper, we construct the wavelet eigenvalue regression methodology in high dimensions. We assume that possibly non-Gaussian, finite-variance $p$-variate measurements are made of a low-dimensional $r$-variate ($r \ll p$) fractional…

Zero-range processes with decreasing jump rates are known to exhibit condensation, where a finite fraction of all particles concentrates on a single lattice site when the total density exceeds a critical value. We study such a process on a…

Gaussian processes can be treated as subsets of a standard Hilbert space, however, the volume size relation between the underlying index space of random processes and its convex hull is not clear. The understanding of such volume size…

We generalise the construction of multivariate Hawkes processes to a possibly infinite network of counting processes on a directed graph $\mathbb G$. The process is constructed as the solution to a system of Poisson driven stochastic…

This paper studies nonparametric estimation of parameters of multivariate Hawkes processes. We consider the Bayesian setting and derive posterior concentration rates. First rates are derived for L1-metrics for stochastic intensities of the…

We discuss the order of the variance on a lattice analogue of the Hammersley process with boundaries, for which the environment on each site has independent, Bernoulli distributed values. The last passage time is the maximum number of…

For $\alpha\geq 1$, let $g:\mathbb N\to\mathbb R_+$ be given by $g(0)=0$, $g(1)=1$, $g(k)=(k/k-1)^\alpha$, $k\geq 2$. Consider the symmetric nearest neighbour zero range process on the discrete torus $\mathbb T_L$ in which a particle jumps…

This paper is devoted to the introduction of a new class of consistent estimators of the fractal dimension of locally self-similar Gaussian processes. These estimators are based on convex combinations of sample quantiles of discrete…

A Hamiltonian system with a modified Henon-Heiles potential is investigated. This describes the motion of free test particles in vacuum gravitational pp-wave spacetimes with both quadratic ("homogeneous") and cubic ("non-homogeneous") terms…

The generation of high-order harmonics in finite, hexagonal nanoribbons is simulated. Ribbons with armchair and zig-zag edges are investigated by using a tight-binding approach with only nearest neighbor hopping. By turning an alternating…

We study the extremal process associated with the Discrete Gaussian Free Field on the square lattice and elucidate how the conformal symmetries manifest themselves in the scaling limit. Specifically, we prove that the joint process of…

In this paper, we develop two stochastic models where the variable under consideration follows Harris distribution. The mean and variance of the processes are derived and the processes are shown to be non-stationary. In the second model,…

We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\textgreater{}1/2$ and multiplicative noise component $\sigma$.…

Coherent time is a characteristic time in the extreme nonlinear optics regime and thus generally introduced as the dephasing time in the simulations of the solid-state high-harmonic generation. This characteristic time linked with the…