New techniques of local sensitivity analysis for nonsmooth generalized equations are applied to the study of sequences of statistical estimates and empirical approximations to solutions of stochastic programs. Consistency is shown to follow from a certain local invertibility property, and asymptotic distributions are derived from a generalized implicit function theorem that characterizes asympt...

We derive high-order terms in the asymptotic expansions of the steadystate voltage potentials in the presence of a finite number of diametrically small inhomogeneities with conductivities different from the background conductivity. Our derivation is rigorous, and based on layer potential techniques. The asymptotic expansions in this paper are valid for inhomogeneities with Lipschitz boundaries ...

SU(N) Yang-Mills theories, which are expected to describe the strong interaction in the case N = 3, are one of the most studied models in theoretical physics. While their asymptotic UV behavior is well under control thanks to asymptotic freedom, the need of non-perturbative techniques to describe the IR behavior has rapidly appeared to be mandatory. The reasons of this non-perturbativity of the...

Abstract A non-integrable, variable coefficient nonlinear Schrödinger equation which governs the nonlinear pulse propagation in an inhomogeneous medium is considered. The same equation is also applicable to optical pulse propagation in averaged, dispersion-managed optical fiber systems, or fiber systems with phase modulation and pulse compression. Multi-scale asymptotic techniques are employed ...

Global asymptotic stability conditions for discrete nonlinear scalar stochastic systems with state delay are obtained based on the convergence theorem for semimartingale inequalities, without assuming the Lipschitz conditions for nonlinear drift functions. The Lyapunov-Krasovskii and degenerate functionals techniques are used. The derived stability conditions are directly expressed in terms of ...

Asymptotic analysis has always been very useful for deriving distributions in statistics in cases where the exact distribution is unavailable. More importantly, asymptotic analysis can also provide insight into the inference process itself, suggesting what information is available and how this information may be extracted. The development of likelihood inference over the past twenty-some years ...

We study the small deviation problem logP(supt∈[0,1] |Xt| 6 ε), as ε → 0, for general Lévy processes X . The techniques enable us to determine the asymptotic rate for general real-valued Lévy processes, which we demonstrate with many examples. As a particular consequence, we show that a Lévy process with non-vanishing Gaussian component has the same (strong) asymptotic small deviation rate as t...

Asymptotic analysis has always been very useful for deriving distributions in statistics in cases where the exact distribution is unavailable. More importantly, asymptotic analysis can also provide insight into the inference process itself, suggesting what information is available and how this information may be extracted. The development of likelihood inference over the past twenty-some years ...

In this article, we investigate a robust version of local linear regression smoothers for stationary and censored stochastic processes by using M-type local polynomial techniques and transformations. Under some regularity conditions, we establish the weak and strong consistency as well as the asymptotic normality of proposed estimators. We propose an easily implemented bandwidth selection crite...

Two techniques for reliably controlling the defect (residual) in the numerical solution of nonstiff initial value problems were given in [D. This work describes an alternative approach based on Hermite-Birkhoff interpolation. The new approach has two main advantagesmit is applicable to Runge-Kutta schemes of any order, and it gives rise to a defect of the optimum asymptotic order of accuracy. F...