Related papers: Exact bounds on epsilon processes
In this paper, we give sufficient conditions to establish central limit theorems for boundary estimates of Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process.…
A wide range of numerical methods exists for computing polynomial approximations of solutions of ordinary differential equations based on Chebyshev series expansions or Chebyshev interpolation polynomials. We consider the application of…
In this paper, we propose the concept of accelerated convergence that has originally been developed to speed up the convergence of numerical methods for extremum seeking (ES) loops. We demonstrate how the dynamics of ES loops may be…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
In this paper, we study the fundamental open question of finding the optimal high-order algorithm for solving smooth convex minimization problems. Arjevani et al. (2019) established the lower bound $\Omega\left(\epsilon^{-2/(3p+1)}\right)$…
We give a $(2 + \epsilon)$-approximation algorithm for minimizing total weighted completion time on a single machine under release time and precedence constraints. This settles a recent conjecture made in [18]
This paper considers online optimization for a system that performs a sequence of back-to-back tasks. Each task can be processed in one of multiple processing modes that affect the duration of the task, the reward earned, and an additional…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…
Consider two independent Poisson point processes of unit intensity in the Euclidean space of dimension $d$ at least 3. We construct a perfect matching between the two point sets that is a factor (i.e., an equivariant measurable function of…
Point processes are an essential tool when we are interested in where in time or space events occur. The basic starting point for point processes is usually the Poisson process. Over the years, Stein's method has been developed with a great…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
We consider a particle system with weights and the scaling limits derived from its occupation time. We let the particles perform independent recurrent L\'evy motions and we assume that their initial positions and weights are given by a…
We show an elementary method to have (finite time and asymptotic) computer assisted explicit upper bounds on convergence to equilibrium (decay of correlations) and escape rate for systems satisfying a Lasota Yorke inequality. The bounds are…
Conformance checking encompasses a body of process mining techniques which aim to find and describe the differences between a process model capturing the expected process behavior and a corresponding event log recording the observed…
There is a long history of approximation schemes for the problem of scheduling jobs on identical machines to minimize the makespan. Such a scheme grants a $(1+\epsilon)$-approximation solution for every $\epsilon > 0$, but the running time…
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…
We point out that EXP3 can be implemented in constant time per round, propose more practical algorithms, and analyze the trade-offs between the regret bounds and time complexities of these algorithms.
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…
Rational best approximations (in a Chebyshev sense) to real functions are characterized by an equioscillating approximation error. Similar results do not hold true for rational best approximations to complex functions in general. In the…
We provide very effective methods to convert both asymptotic and explicit numeric bounds on the prime counting function $\psi(x)$ to bounds of the same type on both $\theta(x)$ and $\pi(x)$. This follows up our previous work on $\psi(x)$ in…