Related papers: Tail bounds via generic chaining
This contribution establishes exact tail asymptotics of $\sup_{(s,t)\in\mathbf{E}}$ $X(s,t)$ for a large class of nonhomogeneous Gaussian random fields $X$ on a bounded convex set $\mathbf{E}\subset\mathbb{R}^2$, with variance function that…
Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…
We provide a generalisation of Pinelis' Rademacher-Gaussian tail comparison to complex coefficients. We also establish uniform bounds on the probability that the magnitude of weighted sums of independent random vectors uniform on Euclidean…
One problem of wide interest involves estimating expected crossing-times. Several tools have been developed to solve this problem beginning with the works of Wald and the theory of sequential analysis. An extension of his approach is…
In this paper we propose a problem-driven scenario generation approach to the single-period portfolio selection problem which use tail risk measures such as conditional value-at-risk. Tail risk measures are useful for quantifying potential…
We prove upper bounds on the transition probabilities of random walks with i.i.d. random conductances with a polynomial lower tail near $0$. We consider both constant and variable speed models. Our estimates are sharp. As a consequence, we…
The best techniques for the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a variety of concave continuous relaxations of the objective function. A standard…
The sums and maxima of non-stationary random length sequences of regularly varying random variables may have the same tail and extremal indices, Markovich and Rodionov (2020). The main constraint is that there exists a unique series in a…
An irreducible stochastic matrix with rational entries has a stationary distribution given by a vector of rational numbers. We give an upper bound on the lowest common denominator of the entries of this vector. Bounds of this kind are used…
We study moderate deviations in the exponential corner growth model, both in the bulk setting and the increment-stationary setting. The main results are sharp right-tail bounds on the last-passage time and the exit point of the…
This work derives extremal tail bounds for the Gaussian trace estimator applied to a real symmetric matrix. We define a partial ordering on the eigenvalues, so that when a matrix has greater spectrum under this ordering, its estimator will…
Stochastic-approximation gradient methods are attractive for large-scale convex optimization because they offer inexpensive iterations. They are especially popular in data-fitting and machine-learning applications where the data arrives in…
In this paper we look at a particular problem related to under-determined linear systems of equations with sparse solutions. $\ell_1$-minimization is a fairly successful polynomial technique that can in certain statistical scenarios find…
We perform a posteriori error analysis in the supremum norm for the quadratic discontinuous Galerkin method for the elliptic obstacle problem. We define two discrete sets (motivated by Gaddam, Gudi and Kamana [1]), one set having integral…
We study the height and width of a Galton--Watson tree with offspring distribution B satisfying E(B)=1, 0 < Var(B) < infinity, conditioned on having exactly n nodes. Under this conditioning, we derive sub-Gaussian tail bounds for both the…
A regularly varying time series as introduced in Basrak and Segers (2009) is a (multivariate) time series such that all finite dimensional distributions are multivariate regularly varying. The extremal behavior of such a process can then be…
While the convergence behaviors of stochastic gradient methods are well understood \emph{in expectation}, there still exist many gaps in the understanding of their convergence with \emph{high probability}, where the convergence rate has a…
We explore the limit of stochastic differential equations driven by some random processes satisfying singularly perturbed second order stochastic differential equations. The main tool we employ is the universal limit theorem in rough path…
Chi-square processes with trend appear naturally as limiting processes in various statistical models. In this paper we are concerned with the exact tail asymptotics of the supremum taken over (0; 1) of a class of locally stationary…
We derive simple but nearly tight upper and lower bounds for the binomial lower tail probability (with straightforward generalization to the upper tail probability) that apply to the whole parameter regime. These bounds are easy to compute…