Related papers: Another Asymptotic Notation : "Almost"
IT systems of today are becoming larger and more complex, rendering their human supervision more difficult. Artificial Intelligence for IT Operations (AIOps) has been proposed to tackle modern IT administration challenges thanks to AI and…
In this note, we are concerned with the asymptotic approximation of a class of double integrals which can be represented as an angular spectrum superposition. These double integrals typically appear in electromagnetic scattering problems.…
Despite growing interest in using large language models (LLMs) to automate annotation, their effectiveness in complex, nuanced, and multi-dimensional labelling tasks remains relatively underexplored. This study focuses on annotation for the…
New asymptotic approximations of the non-central $t$ distribution are given, a generalization of the Student's $t$ distribution. Using new integral representations, we give new asymptotic expansions for large values of the noncentrality…
A variety of estimators for the parameters of the Generalized Pareto distribution, the approximating distribution for excesses over a high threshold, have been proposed, always assuming the underlying data to be independent. We recently…
In this paper, we formulate and prove new properties of conditional quantiles given one of the particular sigma-fields. Next, we use them to investigate almost sure asymptotic behavior of central order statistics which arise from strictly…
We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence…
We consider the fragmentation at nodes of the L\'{e}vy continuous random tree introduced in a previous paper. In this framework we compute the asymptotic for the number of small fragments at time $\theta$. This limit is increasing in…
The purpose of this note is to share some observations and speculations concerning the asymptotic behavior of Gromov-Witten invariants. They may be indicative of some deep phenomena in symplectic topology that in full generality are outside…
We calculate asymptotic expansions for the moments of number of comparisons used by the randomized quick sort algorithm using the singularity analysis of certain generating functions.
In this paper, we study three asymptotic regimes that can be applied to ranking and selection (R&S) problems with general sample distributions. These asymptotic regimes are constructed by sending particular problem parameters (probability…
The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that…
We propose a generalization of the asymptotic equipartition property to discrete sources with an ambiguous alphabet, and prove that it holds for irreducible stationary Markov sources with an arbitrary distinguishability relation. Our…
We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
It is shown the almost sure convergence and asymptotical normality of a generalization of Kesten's stochastic approximation algorithm for multidimensional case. In this generalization, the step increases or decreases if the scalar product…
Bagging is a useful method for large-scale statistical analysis, especially when the computing resources are very limited. We study here the asymptotic properties of bagging estimators for $M$-estimation problems but with massive datasets.…
We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincide with those of processes generating iterated processes.…
This note addresses the input and output of intervals in the sense of interval arithmetic and interval constraints. The most obvious, and so far most widely used notation, for intervals has drawbacks that we remedy with a new notation that…
We enumerate the connected graphs that contain a linear number of edges with respect to the number of vertices. So far, only the first term of the asymptotics was known. Using analytic combinatorics, i.e. generating function manipulations,…