Related papers: Hitting probabilities for general Gaussian process…
This paper investigates extreme value theory for processes obtained by applying transformations to stationary Gaussian processes, also called subordinated Gaussian processes. The main contributions are as follows. First, we refine the…
Although there is an extensive literature on the maxima of Gaussian processes, there are relatively few non-asymptotic bounds on their lower-tail probabilities. The aim of this paper is to develop such a bound, while also allowing for many…
Let $X(t)=(X_1(t), \dots, X_n(t)), t\in \mathcal{T}\subset \mathbb{R} $ be a centered vector-valued Gaussian process with independent components and continuous trajectories, and $h(t)=(h_1(t),\dots, h_n(t)), t\in \mathcal{T} $ be a…
We consider a diffusion process under a local weak H\"{o}rmander condition on the coefficients. We find Gaussian estimates for the density in short time and exponential lower and upper bounds for the probability that the diffusion remains…
Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…
Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference…
We compute the generating function of random planar quadrangulations with three marked vertices at prescribed pairwise distances. In the scaling limit of large quadrangulations, this discrete three-point function converges to a simple…
It is shown that if the Euclidean path integral measure of a minimally coupled free quantum scalar field on a classical metric background is interpreted as probability of observing the field configuration given the background metric then…
We prove that under fairly general conditions properly rescaled determinantal random point field converges to a generalized Gaussian random process.
Let $Z_1,\ldots,Z_n$ be i.i.d. isotropic random vectors in $\mathbb{R}^p$, and $T \subset \mathbb{R}^p$ be a compact set. A classical line of empirical process theory characterizes the size of the suprema of the quadratic process…
Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of automatic relevance determination kernels, but in high-dimensional datasets this approach can be unreliable. A more…
Many physical phenomena are modeled as stochastic searchers looking for targets. In these models, the probability that a searcher finds a particular target, its so-called hitting probability, is often of considerable interest. In this work…
In extreme value statistics, the peaks-over-threshold method is widely used. The method is based on the generalized Pareto distribution characterizing probabilities of exceedances over high thresholds in $\mathbb {R}^d$. We present a…
We study the probability that a random walk started inside a subgraph of a larger graph exits that subgraph (or, equivalently, hits the exterior boundary of the subgraph). Considering the chance a random walk started in the subgraph never…
We present simple, user-friendly bounds for the expected operator norm of a random kernel matrix under general conditions on the kernel function $k(\cdot,\cdot)$. Our approach uses decoupling results for U-statistics and the non-commutative…
Analysis of extremal behavior of stochastic processes is a key ingredient in a wide variety of applications, including probability, statistical physics, theoretical computer science, and learning theory. In this paper, we consider centered…
We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…
We study boundary non-crossing probabilities $$ P_{f,u} := \mathrm P\big(\forall t\in \mathbb T\ X_t + f(t)\le u(t)\big) $$ for continuous centered Gaussian process $X$ indexed by some arbitrary compact separable metric space $\mathbb T$.…
Gaussian processes are widely employed as versatile modelling and predictive tools in spatial statistics, functional data analysis, computer modelling and diverse applications of machine learning. They have been widely studied over…