Related papers: Path regularity of Gaussian processes via small de…

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states, and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies,…

For a large $n\times m$ Gaussian matrix, we compute the joint statistics, including large deviation tails, of generalized and total variance - the scaled log-determinant $H$ and trace $T$ of the corresponding $n\times n$ covariance matrix.…

Let $(Z_n)_{n\in\N}$ be a $d$-dimensional {\it random walk in random scenery}, i.e., $Z_n=\sum_{k=0}^{n-1}Y(S_k)$ with $(S_k)_{k\in\N_0}$ a random walk in $\Z^d$ and $(Y(z))_{z\in\Z^d}$ an i.i.d. scenery, independent of the walk. The…

Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the…

The entropy of an ergodic finite-alphabet process can be computed from a single typical sample path x_1^n using the entropy of the k-block empirical probability and letting k grow with $n$ roughly like log n. We further assume that the…

Given that a stationary Gaussian process is above a high threshold, the length of time it spends before going below that threshold is studied. The asymptotic order is determined by the smoothness of the sample paths, which in turn is a…

Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…

Let $\left\{ Z(n),n\geq 1\right\} $ be a critical Galton-Watson branching process with finite variance for the offspring size of particles. Assuming that $0<Z(n)\leq \varphi (n)$, where either $\varphi (n)=an$ for some $a>0$ or $\varphi…

This paper is concerned with sample size determination methodology for prediction models. We propose combining the individual calculations via a learning-type curve. We suggest two distinct ways of doing so, a deterministic skeleton of a…

We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths. The main results obtained in…

Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…

We study translation-invariant determinantal random point fields on the real line. We prove, under quite general conditions, that the smallest nearest spacings between the particles in a large interval have Poisson statistics as the length…

We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…

Dynamical systems driven by nonlinear delay SDEs with small noise can exhibit important rare events on long timescales. When there is no delay, classical large deviations theory quantifies rare events such as escapes from metastable fixed…

Recent work has established a path-gradient estimator for simple variational Gaussian distributions and has argued that the path-gradient is particularly beneficial in the regime in which the variational distribution approaches the exact…

We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…

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…

Gaussian random processes which variances reach theirs maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximums of theirs trajectories have been evaluated using Double Sum Method…

We study moderate deviations of suprema of parametrized sequences of sample bounded Gaussian processes $\{X _x(t), t\in T _x\}$, and first present recent sharp bounds in simple cases. In the almost periodic case, we prove an approximation…

Time evolution of the decay process of unstable particles is investigated in field theory models. We first formulate how to renormalize the non-decay amplitude beyond perturbation theory and then discuss short-time behavior of very…