The asymptotic behavior of densities related to the supremum of a stable process

If X is a stable process of index α∈(0, 2) whose Lévy measure has density cx−α−1 on (0, ∞), and S1=sup0x)∽Aα−1x−α as x→∞ and P(S1≤x)∽Bα−1ρ−1xαρ as x↓0. [Here ρ=P(X1>0) and A and B are known constants.] It is also known that S1 has a continuous density, m say. The main point of this note is to show that m(x)∽Ax−(α+1) as x→∞ and m(x)∽Bxαρ−1 as x↓0. Similar results are obtained for related densities.

Asymptotic gravity wave drag expressions for non-hydrostatic rotating flow over a ridge

Asymptotic expressions are derived for the mountain wave drag in flow with constant wind and static stability over a ridge when both rotation and non-hydrostatic effects are important. These expressions, which are much more manageable than the corresponding exact drag expressions (when these do exist) are found to provide accurate approximations to the drag, even when non-hydrostatic and rotation effects are strong, despite having been developed for cases where these effects are weak. The derived expressions are compared with approximations to the drag found previously, and their asymptotic behaviour in various limits is studied.

Asymptotic behavior at infinity of solutions of multidimensional second kind integral equations

We consider second kind integral equations of the form x(s) - (abbreviated x - K x = y ), in which Ω is some unbounded subset of Rn. Let Xp denote the weighted space of functions x continuous on Ω and satisfying x (s) = O(|s|-p ),s → ∞We show that if the kernel k(s,t) decays like |s — t|-q as |s — t| → ∞ for some sufficiently large q (and some other mild conditions on k are satisfied), then K ∈ B(XP) (the set of bounded linear operators on Xp), for 0 ≤ p ≤ q. If also (I - K)-1 ∈ B(X0) then (I - K)-1 ∈ B(XP) for 0 < p < q, and (I- K)-1∈ B(Xq) if further conditions on k hold. Thus, if k(s, t) = O(|s — t|-q). |s — t| → ∞, and y(s)=O(|s|-p), s → ∞, the asymptotic behaviour of the solution x may be estimated as x (s) = O(|s|-r), |s| → ∞, r := min(p, q). The case when k(s,t) = к(s — t), so that the equation is of Wiener-Hopf type, receives especial attention. Conditions, in terms of the symbol of I — K, for I — K to be invertible or Fredholm on Xp are established for certain cases (Ω a half-space or cone). A boundary integral equation, which models three-dimensional acoustic propaga-tion above flat ground, absorbing apart from an infinite rigid strip, illustrates the practical application and sharpness of the above results. This integral equation mod-els, in particular, road traffic noise propagation along an infinite road surface sur-rounded by absorbing ground. We prove that the sound propagating along the rigid road surface eventually decays with distance at the same rate as sound propagating above the absorbing ground.

A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance plane

A generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived. The expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance, including the limiting cases of zero and infinite impedance. The technique used is a rigorous application of the modified steepest descent method of Ot

On asymptotic behavior at infinity and the finite section method for integral equations on the half-line

e consider integral equations on the half-line of the form and the finite section approximation to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e. exists and is uniformly bounded in the space of bounded continuous functions for all sufficiently large β), then it is stable also for a perturbed equation in which the kernel k is replaced by k + h. The class of perturbations allowed includes all compact and some non-compact perturbations of the integral operator. Using this result we study the stability and convergence of the finite section method in the space of continuous functions x for which ()()()=−∫∞dttxt,sk)s(x0()syβxβx()sxsp+1 is bounded. With the additional assumption that ()(tskt,sk−≤ where ()()(),qsomefor,sassOskandRLkq11>+∞→=∈− we show that the finite-section method is stable in the weighted space for ,qp≤≤0 provided it is stable on the space of bounded continuous functions. With these results we establish error bounds in weighted spaces for x - xβ and precise information on the asymptotic behaviour at infinity of x. We consider in particular the case when the integral operator is a perturbation of a Wiener-Hopf operator and illustrate this case with a Wiener-Hopf integral equation arising in acoustics.

Large time behaviour for functional differential equations with dominant eigenvalues of arbitrary order

The spectral theory for linear autonomous neutral functional differential equations (FDE) yields explicit formulas for the large time behaviour of solutions. Our results are based on resolvent computations and Dunford calculus, applied to establish explicit formulas for the large time behaviour of solutions of FDE. We investigate in detail a class of two-dimensional systems of FDE. (C) 2009 Elsevier Inc. All rights reserved.

Asymptotic Skewness in Exponential Family Nonlinear Models

In this article, we give an asymptotic formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in exponencial family nonlinear models. We generalize the result by Cordeiro and Cordeiro ( 2001). The formula is given in matrix notation and is very suitable for computer implementation and to obtain closed form expressions for a great variety of models. Some special cases and two applications are discussed.

Asymptotic skewness in Birnbaum-Saunders nonlinear regression models

The family of distributions proposed by Birnbaum and Saunders (1969) can be used to model lifetime data and it is widely applicable to model failure times of fatiguing materials. We give a simple matrix formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in Birnbaum-Saunders nonlinear regression models, recently introduced by Lemonte and Cordeiro (2009). The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors, in order to obtain closed-form skewness in a wide range of nonlinear regression models. Empirical and real applications are analyzed and discussed. (C) 2010 Elsevier B.V. All rights reserved.

Asymptotic efficiency in an instrumental variable model

Esta dissertação se propõe ao estudo de inferência usando estimação por método generalizado dos momentos (GMM) baseado no uso de instrumentos. A motivação para o estudo está no fato de que sob identificação fraca dos parâmetros, a inferência tradicional pode levar a resultados enganosos. Dessa forma, é feita uma revisão dos mais usuais testes para superar tal problema e uma apresentação dos arcabouços propostos por Moreira (2002) e Moreira & Moreira (2013), e Kleibergen (2005). Com isso, o trabalho concilia as estatísticas utilizadas por eles para realizar inferência e reescreve o teste score proposto em Kleibergen (2005) utilizando as estatísticas de Moreira & Moreira (2013), e é obtido usando a teoria assintótica em Newey & McFadden (1984) a estatística do teste score ótimo. Além disso, mostra-se a equivalência entre a abordagem por GMM e a que usa sistema de equações e verossimilhança para abordar o problema de identificação fraca.

Non-asymptotic confidence bounds for the optimal value of a stochastic program

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds for the optimal value of the problem which are essentially better than the quality of the corresponding optimal solutions. At the same time, such bounds are more reliable than “standard” confidence bounds obtained through the asymptotic approach. We also discuss bounding the optimal value of MinMax Stochastic Optimization and stochastically constrained problems. We conclude with a small simulation study illustrating the numerical behavior of the proposed bounds.

Search schemes for random optimization algorithms that preserve the asymptotic distribution

Markovian algorithms for estimating the global maximum or minimum of real valued functions defined on some domain Omega subset of R-d are presented. Conditions on the search schemes that preserve the asymptotic distribution are derived. Global and local search schemes satisfying these conditions are analysed and shown to yield sharper confidence intervals when compared to the i.i.d. case.

Spatio-temporal dynamics and transition from asymptotic equilibrium to bounded oscillations in Chrysomya albiceps (Diptera, Calliphoridae)

The sensitivity of parameters that govern the stability of population size in Chrysomya albiceps and describe its spatial dynamics was evaluated in this study. The dynamics was modeled using a density-dependent model of population growth. Our simulations show that variation in fecundity and mainly in survival has marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations. C. albiceps exhibits a two-point limit cycle, but the introduction of diffusive dispersal induces an evident qualitative shift from two-point limit cycle to a one fixed-point dynamics. Population dynamics of C. albiceps is here compared to dynamics of Cochliomyia macellaria, C. megacephala and C. putoria.