Related papers: Unitary transformations, empirical processes and d…
As an example for the fast calculation of distributional parameters of Gaussian processes, we propose a new Monte Carlo algorithm for the computation of quantiles of the supremum norm of weighted Brownian bridges. As it is known, the…
Strong embeddings, that is, couplings between a partial sum process of a sequence of random variables and a Brownian motion, have found numerous applications in probability and statistics. We extend Chatterjee's novel use of Stein's method…
In a previous work, the first and third authors studied a random knot model for all two-bridge knots using billiard table diagrams. Here we present a closed formula for the distribution of the crossing numbers of such random knots. We also…
Motivated by applications in trajectory inference and particle tracking, we introduce Smooth Schr\"odinger Bridges. Our proposal generalizes prior work by allowing the reference process in the Schr\"odinger Bridge problem to be a smooth…
We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class…
We investigate the Brown measures of compressions of $R$-diagonal random variables, extending previous results to include unbounded cases. For random variables with finite variance, we demonstrate that the Brown measures of their…
We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient…
Motivated by the connection between the Kyle equilibrium with static private signal and the Brownian bridge, we study a much broader class of bridges that allow one to consider more general equilibrium models, for example ones including…
Flow matching and diffusion bridge models have emerged as leading paradigms in generative speech enhancement, modeling stochastic processes between paired noisy and clean speech signals based on principles such as flow matching, score…
In the common time series model $X_{i,n} = \mu (i/n) + \varepsilon_{i,n}$ with non-stationary errors we consider the problem of detecting a significant deviation of the mean function $\mu$ from a benchmark $g (\mu )$ (such as the initial…
We prove that the random empirical measure of appropriately rescaled particle trajectories of the interchange process on path graphs converges weakly to the deterministic measure of stationary Brownian motion on the unit interval. This is a…
Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…
We obtain sufficient conditions of stochastic equivalence of Gaussian random fields with special covariance function. These results generalize Doob's transformation (condition of stochastic equivalence of a Gaussian and a Wiener processes)…
In this paper, we present a general framework for testing relevant hypotheses in functional time series. Our unified approach covers one-sample, two-sample, and change point problems under contaminated observations with arbitrary sampling…
Despite recent advances in population-based structural health monitoring (PBSHM), knowledge transfer between highly-disparate structures (i.e., heterogeneous populations) remains a challenge. The current work proposes that heterogeneous…
A simple two-species asymmetric exclusion model in one dimension with bulk and boundary exchanges of particles is investigated for the existence of spontaneous symmetry breaking. The model is a generalization of the bridge model for which…
The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…
We propose simple methods for multivariate diffusion bridge simulation, which plays a fundamental role in simulation-based likelihood and Bayesian inference for stochastic differential equations. By a novel application of classical coupling…
Permutation tests are a popular choice for distinguishing distributions and testing independence, due to their exact, finite-sample control of false positives and their minimax optimality when paired with U-statistics. However, standard…
Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…