相关论文: Asymptotic expansion for inverse moments of binomi…

Let $p(n)$ denote the partition function. In this paper our main goal is to derive an asymptotic expansion up to order $N$ (for any fixed positive integer $N$) along with estimates for error bounds for the shifted quotient of the partition…

Asymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given…

General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams.

This work gives a general approach to the determination of the asymptotic behavior of the sums of functions of primes based on the distribution of primes. It refines the estimate of the remainder term of the asymptotic expansion of the sums…

Given a set of independent Poisson random variables with common mean, we study the distribution of their maximum and obtain an accurate asymptotic formula to locate the most probable value of the maximum. We verify our analytic results with…

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…

We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are developed.

Asymptotic distribution for the proportional covariance model under multivariate normal distributions is derived. To this end, the parametrization of the common covariance matrix by its Cholesky root is adopted. The derivations are made in…

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 [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the…

Project a collection of points on the high-dimensional sphere onto a random direction. If most of the points are sufficiently far from one another in an appropriate sense, the projection is locally close in distribution to the Poisson point…

We propose a new method for obtaining complete asymptotic expansions in a systematic manner, which is suitable for counting sequences of various graph families in dense regime. The core idea is to encode the two-dimensional array of…

The algebraic properties of formal power series, whose coefficients show factorial growth and admit a certain well-behaved asymptotic expansion, are discussed. It is shown that these series form a subring of $\mathbb{R}[[x]]$. This subring…

Asymptotic expansions are derived for associated Legendre functions of degree $\nu$ and order $\mu$, where one or the other of the parameters is large. The expansions are uniformly valid for unbounded real and complex values of the argument…

We establish formulas for the constant factor in several asymptotic estimates related to the distribution of integer and polynomial divisors. The formulas are then used to approximate these factors numerically.

In this paper, insight is given in the techniques used to compute asymptotic expansions. In a broad fashion the technique is described. Most of the results apply to the paper "An expansion for the maximum likelihood estimator and its…

In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…

This work consists in the asymptotic analysis of the solution of Poisson equation in a bounded domain of $\mathbb{R}^{P}$ $(P=2,3)$ with a thin layer. We use a method based on hierarchical variational equations to derive asymptotic…

In [8], asymptotic expansion of the martingale with mixed normal limit was provided. The expansion formula is expressed by the adjoint of a random symbol with coefficients described by the Malliavin calculus, differently from the standard…

In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution…