Related papers: U-statistics in stochastic geometry
A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal…
This note provides an introduction to molecular dynamics, the computational implementation of the theory of statistical physics. The discussion is focused on the properties of Langevin dynamics, a degenerate stochastic differential equation…
A uniform in probability approximation is established for Studentized processes of non degenerate U-statistics of order m greater or equal to 2 in terms of a standard Wiener process. The classical condition that the second moment of kernel…
We introduce a stochastic analysis of Grassmann random variables suitable for the stochastic quantization of Euclidean fermionic quantum field theories. Analysis on Grassmann algebras is developed here from the point of view of quantum…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the…
In this work we study the one-dimensional stochastic Kimura equation $\partial_{t}u\left(z,t\right)=z\partial_{z}^{2}u\left(z,t\right)+u\left(z,t\right)\dot{W}\left(z,t\right)$ for $z,t>0$ equipped with a Dirichlet boundary condition at…
This paper develops the large deviations theory for the point process associated with the Euclidean volume of $k$-nearest neighbor balls centered around the points of a homogeneous Poisson or a binomial point processes in the unit cube. Two…
This paper develops a general framework for analyzing asymptotics of $V$-statistics. Previous literature on limiting distribution mainly focuses on the cases when $n \to \infty$ with fixed kernel size $k$. Under some regularity conditions,…
Special case of a Gibbsian facet process on a fixed window with a discrete orientation distribution and with increasing intensity of the underlying Poisson process is studied. All asymptotic moments for interaction U-statistics are…
Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific…
Consider an unlimited homogeneous medium disturbed by points generated via Poisson process. The neighborhood of a point plays an important role in spatial statistics problems. Here, we obtain analytically the distance statistics to $k$th…
We consider a random variable expressed as the Euclidean distance between an arbitrary point and a random variable uniformly distributed in a closed and bounded set of a three-dimensional Euclidean space. Four cases are considered for this…
The family of U-statistics plays a fundamental role in statistics. This paper proves a novel exponential inequality for U-statistics under the time series setting. Explicit mixing conditions are given for guaranteeing fast convergence, the…
We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random…
We construct examples of degree-two U- and V-statistics of $n$ i.i.d.~heavy-tailed random vectors in $\mathbb{R}^{d(n)}$, whose $\nu$-th moments exist for ${\nu > 2}$, and provide tight bounds on the error of approximating both statistics…
We study the convergence of stochastic fixed point iterations in the consistent case (in the sense of Butnariu and Fl{\aa}m (1995)) in several different settings, under decreasingly restrictive regularity assumptions of the fixed point…
A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time.…
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…