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The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…
We study the joint asymptotics of forward and backward processes of numbers of non-empty urns in an infinite urn scheme. The probabilities of balls hitting the urns are assumed to satisfy the conditions of regular decrease. We prove weak…
We establish higher-order nonasymptotic expansions for a difference between probability distributions of sums of i.i.d. random vectors in a Euclidean space. The derived bounds are uniform over two classes of sets: the set of all Euclidean…
Uniform asymptotic expansions are derived for the zeros of the reverse generalized Bessel polynomials of large degree $n$ and real parameter $a$. It is assumed that $-\Delta_{1} n+\frac{3}{2} \leq a \leq \Delta_{2} n$ for fixed arbitrary…
Understanding rare events is critical across domains ranging from signal processing to reliability and structural safety, extreme-weather forecasting, and insurance. The analysis of rare events is a computationally challenging problem,…
In statistical physics and information theory, although the exponent of the partition function is often of our primary interest, there are cases where one needs more detailed information. In this paper, we present a general framework to…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Let $\{X(t) : t \in [0, \infty) \}$ be a centered stationary Gaussian process. We study the exact asymptotics of $\pr (\sup_{s \in [0,T]} X(t) > u)$, as $u \to \infty$, where $T$ is an independent of \{X(t)\} nonnegative random variable. It…
Matrix completion algorithms recover a low rank matrix from a small fraction of the entries, each entry contaminated with additive errors. In practice, the singular vectors and singular values of the low rank matrix play a pivotal role for…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
Inference on the parametric part of a semiparametric model is no trivial task. If one approximates the infinite dimensional part of the semiparametric model by a parametric function, one obtains a parametric model that is in some sense…
In this paper we develop non-asymptotic Gaussian approximation results for the sampling distribution of suprema of empirical processes when the indexing function class $\mathcal{F}_n$ varies with the sample size $n$ and may not be Donsker.…
We derive source integrals for multipole moments that describe the behaviour of static and axially symmetric spacetimes close to spatial infinity. We assume isolated non-singular sources but will not restrict the matter content otherwise.…
An asymptotic theory is developed for computing volumes of regions in the parameter space of a directed Gaussian graphical model that are obtained by bounding partial correlations. We study these volumes using the method of real log…
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…
We consider a joint asymptotic framework for studying semi-nonparametric regression models where (finite-dimensional) Euclidean parameters and (infinite-dimensional) functional parameters are both of interest. The class of models in…
This work is concerned with the analysis of a stochastic approximation algorithm for the simulation of quasi-stationary distributions on finite state spaces. This is a generalization of a method introduced by Aldous, Flannery and Palacios.…
Impropriety testing for complex-valued vector has been considered lately due to potential applications ranging from digital communications to complex media imaging. This paper provides new results for such tests in the asymptotic regime,…