The asymptotic high momentum behaviour of quantum field theories with cubic interactions is investigated using renormalization group techniques in the asymmetric limit x ≪ 1. Particular emphasis is paid to theories with interactions involving more than one field where it is found that a matrix renormalization is necessary. Asymptotic scaling forms, in agreement with Regge theory, are derived fo...

Intercept and deterministic trend functions are known to have a substantial effect on cointegration analysis, and notably on the asymptotic distributions of various test statistics. In this paper we propose a unifying approach to the analysis of cointegrated vector autoregressions by allowing for a wide class of trend functions. Next, estimates of these trends are incorporated in the asymptotic...

Sergey Pinchuk discovered a class of pairs of real polynomials in two variables that have a nowhere vanishing Jacobian determinant and define maps of the real plane to itself that are not one-to-one. This paper describes the asymptotic behavior of one specific map in that class. The level of detail presented permits a good geometric visualization of the map. Errors in an earlier description of ...

In a general command tracking and disturbance rejection problem, it is known that a sampled-data controller using zero-order hold may only guarantee asymptotic tracking at the sampling instances, but in general cannot guarantee the absence of ripples between the sampling instants. In this paper, a discrete robust regulator and a sampled-data robust regulator using slide modes techniques and exp...

This paper investigates the performance of finite blocklength codes over general classes of channels. In particular, results on the maximum achievable rate at a particular blocklength and a target error probability are presented. A new converse result is also presented, and it is shown that in a number of cases, the bounds are quite tight. In brief, the results in the paper may be divided into ...

By using a change of scale and space, we study a class of stochastic differential equations (SDEs) whose solutions are drift–perturbed and exhibit asymptotic behaviour similar to standard Brownian motion. In particular sufficient conditions ensuring that these processes obey the Law of the Iterated Logarithm (LIL) are given. Ergodic–type theorems on the average growth of these non-stationary pr...

Quadratic regression functionals are important for bandwidth selection of nonparametric regression techniques and for nonparametric goodness-of-t test. Based on local polynomial regression , we propose estimators for weighted integrals of squared derivatives of regression functions. The rates of convergence in mean square error are calculated under various degrees of smoothness and appropriate ...

We consider several model problems from a class of elliptic perturbation equations in two dimensions. The domains, the diierential operators, the boundary conditions, and so on, are rather simple, and are chosen in a way that the solutions can be obtained in the form of integrals or Fourier series. By using several techniques from asymptotic analysis (saddle point methods, for instance) we try ...

We investigate some real time behaviour of a (discrete time) single server system with nonpreemptive LCFS task scheduling . The main results deal with the probability distribution of a random variable SRD(T), which describes the time the system operates without any violation of a fixed task service time deadline T . A tree approach, similar to those already used for the derivation of the same q...

This paper studies the asymptotic properties of partitioning estimators of the conditional expectation function and its derivatives. Mean-square and uniform convergence rates are established and shown to be optimal under simple and intuitive conditions. The uniform rate explicitly accounts for the effect of moment assumptions, which is useful in semiparametric inference. A general asymptotic in...