Abstract: Let X be a Kotz Type III elliptical random vector in IR, k ≥ 2, and let tn, n ≥ 1 be positive constants such that limn→∞ tn = ∞. In this article we obtain an asymptotic expansion of the tail probability P {X > tna},a ∈ IR. As an application we derive an approximation for the conditional excess distribution. Furthermore, we discuss the asymptotic dependence of Kotz Type III triangular ...

In this paper the class of ARCH(∞) models is generalized to the nonstationary class of ARCH(∞) models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation “locally stationary ARCH(∞) process.” The asymptotic properties of weighted quasi-likelihood estimators of time-varying ARCH(p) processes (p < ∞) are studied, including asymptotic ...

The electrical dc-conductivity of disordered, noninteracting electrons is calculated in the asymptotic limit of high lattice dimensions d→` . To go beyond the lowest-order contribution in the expansion parameter 1/d of the single bubble diagram, vertex corrections are calculated from an asymptotic expression for the two-particle vertex. A mean-field approximation for the dc conductivity contain...

We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials Bn(x;λ) in detail. The starting point is their Fourier series on [0, 1] which, it is shown, remains valid as an asymptotic expansion over compact subsets of the complex plane. This is used to determine explicit estimates on the constants in the approximation, and also to analyze oscillatory phenomena which arise in certain ...

Generalized Bose-Einstein and Fermi-Dirac distributions in nonextensive quantum statistics have been discussed by the maximum-entropy method (MEM) with the optimum Lagrange multiplier based on the exact integral representation [A. K. Rajagopal, R. S. Mendes, and E. K. Lenzi, Phys. Rev. Lett. 80, 3907 (1998)]. It has been shown that the (q-1) expansion in the exact approach agrees with the resul...

We propose an information theoretic approach to approximating asymptotic distributions of statistics using the maximum entropy densities. Conventional maximum entropy densities are typically defined on a bounded support. For distributions defined on unbounded supports, we propose to use an asymptotically negligible dampening function for the maximum entropy approximation such that it is well de...

We consider Brownian motion in a bounded domain Ω on a twodimensional Riemannian manifold (Σ, g). We assume that the boundary ∂Ω is smooth and reflects the trajectories, except for a small absorbing arc ∂Ωa ⊂ ∂Ω. As ∂Ωa is shrunk to zero the expected time to absorption in ∂Ωa becomes infinite. The narrow escape problem consists in constructing an asymptotic expansion of the expected lifetime, d...

The behavior of a point particle traveling with a constant speed in a region D ∈ RN , undergoing elastic collisions at the regions’s boundary, is known as the billiard problem. Various billiard models serve as approximation to the classical and semi-classical motion in systems with steep potentials (e.g. for studying classical molecular dynamics, cold atom’s motion in dark optical traps and mic...

‎we obtain the asymptotic expansion of the sequence with general term $frac{a_n}{g_n}$‎, ‎where $a_n$ and $g_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎also‎, ‎we obtain some explicit bounds concerning $g_n$ and $frac{a_n}{g_n}$.

Abstract We show that solutions for a specifically scaled nonlinear wave equation of elasticity converge to linear Euler–Bernoulli beam system. construct an approximation the solution, using suitable asymptotic expansion ansatz based upon one-dimensional equation. Following this, we derive existence appropriately initial data and can bound difference between analytical solution approximating se...