相关论文: Quantifying the threshold phenomena for propagatio…

We consider statistical inference for a class of dynamic mixed-effect models described by stochastic differential equations whose drift and diffusion coefficients simultaneously depend on fixed- and random-effect parameters. Assuming that…

An integro-differential expression for the diffusion current of the impurities diffusing by the mechanism of bound impurity-defect pairs has been derived. The ensuing nonlocal diffusion equation generalizes the existing theories of…

We offer in this paper the non-asymptotical bilateral sharp exponential estimates for tail of maximum distribution of {\it discontinuous} random fields. Our consideration based on the theory of Prokhorov-Skorokhod spaces of random fields…

Accurately assessing financial risk requires capturing both individual asset volatility and the complex, asymmetric dependence structures that emerge during extreme market events. While modern diffusion-based models have advanced…

The problem of flame propagation is studied as an example of unstable fronts that wrinkle on many scales is studied. The analytic tool of pole expansion in the complex plane is emloyed to address the interaction of the unstable growth…

The purpose of the paper is to find explicit formulas describing the joint distributions of the first hitting time and place for half-spaces of codimension one for a diffusion in $\R^{n+1}$, composed of one-dimensional Bessel process and…

We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion…

In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…

In presence of long range dispersal, epidemics spread in spatially disconnected regions known as clusters. Here, we characterize exactly their statistical properties in a solvable model, in both the supercritical (outbreak) and critical…

These notes are based on the lectures given in a mini-course at VIASM (Vietnam Institute for Advanced Study in Mathematics) 2025 Summer School. They give a brief account of the theory (with detailed proofs) for propagation governed by a…

This paper is concerned with the processes of spatial propagation and penetration of turbulence from the regions where it is locally excited into initially laminar regions. The phenomenon has come to be known as "turbulence spreading" and…

We present a consistent theoretical approach for calculating effective nonlinear susceptibilities of metamaterials taking into account both frequency and spatial dispersion. Employing the discrete dipole model, we demonstrate that effects…

Non-locality can be quantified by the violation of a Bell inequality. Since this violation may be amplified by local operations an alternative measure has been proposed - distillable non-locality. The alternative measure is difficult to…

We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper…

We explore some properties of the conditional distribution of an i.i.d. sample under large exceedances of its sum. Thresholds for the asymptotic independance of the summands are observed, in contrast with the classical case when the…

In this paper we study nonlocal problems that are analogous to the local ones given by the Laplacian or the p-Laplacian with dynamical boundary conditions. We deal both with smooth and with singular kernels and show existence and uniqueness…

A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts.…

We study the wave propagation in nonlinear electrodynamical models. Particular attention is paid to the derivation and the analysis of the Fresnel equation for the wave covectors. For the class of general nonlinear Lagrangian models, we…

We study a class of nonlocal-diffusion equations with drifts, and derive a priori $\Phi$-H\"older estimate for the solutions by using a purely probabilistic argument, where $\Phi$ is an intrinsic scaling function for the equation.

The probability distribution of percolation thresholds in finite lattices were first believed to follow a normal Gaussian behaviour. With increasing computer power and more efficient simulational techniques, this belief turned to a…