Related papers: Approximation and bounds for the Wallis ratio
This paper explores the asymptotic behaviour of the radii of convexity and uniform convexity for normalized Bessel functions with respect to large order. We provide detailed asymptotic expansions for these radii and establish recurrence…
We present non-asymptotic two-sided bounds to the log-marginal likelihood in Bayesian inference. The classical Laplace approximation is recovered as the leading term. Our derivation permits model misspecification and allows the parameter…
In this paper we establish a general asymptotic formula for the sum of the first $n$ prime numbers, which leads to a generalization of the most accurate asymptotic formula given by Massias and Robin. Further we prove a series of results…
The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The…
We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…
The paper considers a universal approach that allows one to quite simply obtain nonlinear asymptotic estimates of various summation functions. It is shown the application of this approach to the asymptotic estimation of divergent Dirichlet…
We consider the random continued fraction S(t) := 1/(s_1 + t/(s_2 + t/(s_3 + >...))) where the s_n are independent random variables with the same gamma distribution. For every realisation of the sequence, S(t) defines a Stieltjes function.…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
We study finite sections of weighted Hardy's inequality following the approach of De Bruijn. Similar to the unweighted case, we obtain an asymptotic expression for the optimal constant.
We derive uniform and non-uniform asymptotics of the Charlier polynomials by using difference equation methods alone. The Charlier polynomials are special in that they do not fit into the framework of the turning point theory, despite the…
We consider time-harmonic Maxwell's equations set in an heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in $L^2$, we provide a frequency-explicit approximability estimate…
We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalized fluctuation process of the digit sums converges strongly distributional to a random variable…
A determinantal approximation is obtained for the permanent of a doubly stochastic matrix. For moderate-deviation matrix sequences, the asymptotic relative error is of order $O(n^{-1})$.
The system of equations for parametric sub-resonant growth of the amplitude of oscillations was obtained. The time of turning point from the growing of the amplitude to the bounded oscillations in the slow variable was found. The comparison…
The method of extrapolating asymptotic series, based on the Self-Similar Approximation Theory, is developed. Several important questions are answered, which makes the foundation of the method unambiguous and its application straightforward.…
The nearest integer continued fraction of a real number $x$ from $[-1/2, 1/2)$ is defined. Some metrical properties of these expansions are presented. We define the approximation coefficients and give an important result on them. The main…
Thomas' partial likelihood estimator of regression parameters is widely used in the analysis of nested case-control data with Cox's model. This paper proposes a new estimator of the regression parameters, which is consistent and…
The aim of this paper is to investigate in detail the known large argument asymptotic series of the Lommel function by Stieltjes transform representations. We obtain a number of properties of this asymptotic expansion, including explicit…
This contribution summarizes the results on the asymptotic performance of several variants of the FastICA algorithm. A number of new closed-form expressions are presented.
We suggest a continued fraction origin to Ramanujan's approximation to {(a-b)/(a+b)}^2 in terms of the arc length of an ellipse with semiaxes a and b. Moreover, we discuss the asymptotic accuracy of the approximation.