Asymptotic behavior of the OLS estimator for regressions with two slowly varying regressors is studied. It is shown that the asymptotic distribution may belong to one of four types depending on the relative rates of growth of the regressors. The paper expands and corrects recent results by P.C.B.Phillips (2007).

We prove local limit theorems for Gibbs-Markov processes in the domain of attraction of normal distributions. x1 Introduction It is well known that a random variable X belongs to the domain of attraction of a normal distribution DA(2) if its characteristic function satisses () log E exppitX] = itt ? 1 2 t 2 L(1=jtj) for some slowly varying function L : R + ! R + which is bounded below and some ...

We develop a new envelope-function formalism to describe electrons in slowly-varying inhomogeneously strained semiconductor crystals. A coordinate transformation is used to map a deformed crystal back to a geometrically undeformed structure with deformed crystal potential. The single-particle Schrödinger equation is solved in the undeformed coordinates using envelope function expansion, wherein...

It is known that, if an equilibrium of a nonlinear system has a stability property when an external input is frozen, then the property is maintained under the input being slowly varying. In this paper, we show that the same stability property is preserved not only under slowly varying input but also under slowlyvarying-average input (which is not actually slowly varying but its ‘average’ is slo...

Several brain disorders are characterized by abnormally strong neuronal synchrony. Coordinated Reset (CR) stimulation was developed to selectively counteract abnormal neuronal synchrony by desynchronization. For this, phase resetting stimuli are delivered to different subpopulations in a timely coordinated way. In neural networks with spike timing-dependent plasticity CR stimulation may eventua...