Related papers: Parameter estimations for the Gaussian process wit…
This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean…
We prove Gaussian tail estimates for the transition probability of $n$ particles evolving as symmetric exclusion processes on $\bb Z^d$, improving results obtained in \cite{l}. We derive from this result a non-equilibrium Boltzmann-Gibbs…
We consider non-parametric Bayesian estimation of the drift coefficient of a one-dimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions that are…
A functional method for calculating averages of the time-ordered exponential of a continuous isotropic random $N\times N$ matrix process is presented. The process is not assumed to be Gaussian. In particular, the Lyapunov exponents and…
For a scalar Gaussian process $B$ on $\mathbb{R}_{+}$ with a prescribed general variance function $\gamma^{2}\left(r\right) =\mathrm{Var}\left(B\left(r\right) \right) $ and a canonical metric $\mathrm{E}[\left(B\left(t\right)…
We obtain solutions to conservation laws under any random initial conditions that are described by Gaussian stochastic processes (in some cases discretized). We analyze the generalization of Burgers' equation for a smooth flux function…
Quantitative limit theorems for non-linear functionals on the Wiener space are considered. Given the possibly infinite sequence of kernels of the chaos decomposition of such a functional, an estimate for different probability distances…
We study two one-parameter families of point processes connected to random matrices: the Sine_beta and Sch_tau processes. The first one is the bulk point process limit for the Gaussian beta-ensemble. For beta=1, 2 and 4 it gives the limit…
We establish asymptotically Gaussian fluctuations for functionals of a large class of spin models and strongly correlated random point fields, achieving near-optimal rates. For spin models, we demonstrate Gaussian asymptotics for the…
A desirable property of an autocovariance estimator is to be robust to the presence of additive outliers. It is well-known that the sample autocovariance, being based on moments, does not have this property. Hence, the use of an…
In this article, we study the extremal processes of branching Brownian motions conditioned on having an unusually large maximum. The limiting point measures form a one-parameter family and are the decoration point measures in the extremal…
We derive two-sided bounds for moments of random multilinear forms (random chaoses) with nonnegative coeficients generated by independent nonnegative random variables $X_i$ which satisfy the following condition on the growth of moments:…
We show that a necessary and sufficient condition for the sum of iid random vectors to converge (under appropriate shifting and scaling) to a multivariate Gaussian distribution is that the truncated second moment matrix is slowly varying at…
Accurate assessment of systematic uncertainties is an increasingly vital task in physics studies, where large, high-dimensional datasets, like those collected at the Large Hadron Collider, hold the key to new discoveries. Common approaches…
We provide posterior contraction rates for constrained deep Gaussian processes in non-parametric density estimation and classication. The constraints are in the form of bounds on the values and on the derivatives of the Gaussian processes…
A finite point process is characterized by the distribution of the number of points (the size) of the process. In some applications, for example, in the context of packet flows in modern communication networks, it is of interest to infer…
The first passage time process of a L\'evy subordinator with heavy-tailed L\'evy measure has long-range dependent paths. The random fluctuations that appear under two natural schemes of summation and time scaling of such stochastic…
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…
We consider the problem of efficient estimation of the drift parameter of an Ornstein-Uhlenbeck type process driven by a L\'{e}vy process when high-frequency observations are given. The estimator is constructed from the time-continuous…
In the present paper and the companion paper [8] a probabilistic (statistical mechanical) approach to the study of canonical metrics and measures on a complex algebraic variety X is introduced. On any such variety with positive Kodaira…