The aim of this paper is to present a framework for asymptotic analysis of likelihood ratio and minimum discrepancy test statistics. First order asymptotics are presented in a general framework under minimal regularity conditions and for not necessarily nested models. In particular, these asymptotics give sufficient and in a sense necessary conditions for asymptotic normality of test statistics...

The instanton–antiinstanton pair induced asymptotics of perturbation theory expansion for QCD correlators is considered. It is argued that though the true asymptotics is dominated by renormalon, the instanton-induced contribution may dominate in the intermediate asymptotics n = 5÷ 15. Obtained asymptotic formulae are valid for Nf ≤ Nc. For Nf = Nc the finite nonperturbative expression for insta...

We investigate the long time asymptotics in L+(R) for solutions of general nonlinear diffusion equations ut = ∆φ(u). We describe, for the first time, the intermediate asymptotics for a very large class of non-homogeneous nonlinearities φ for which long time asymptotics cannot be characterized by self-similar solutions. Scaling the solutions by their own second moment (temperature in the kinetic...

We investigate pinning regions and unpinning asymptotics in nonlocal equations. We show that phenomena are related to but different from pinning in discrete and inhomogeneous media. We establish unpinning asymptotics using geometric singular perturbation theory in several examples. We also present numerical evidence for the dependence of unpinning asymptotics on regularity of the nonlocal convo...

In this expository article we describe the asymptotics of certain Fredholm determinants which provide solutions to the cylindrical Toda equations, and we explain how these asymptotics are derived. The connection with Fredholm determinants arising in the theory of random matrices, and their asymptotics, are also discussed.

This paper considers error probabilities of random codes for memoryless channels in the fixed-rate regime. Random coding is a fundamental scheme to achieve the channel capacity and many studies have been conducted for the asymptotics of the decoding error probability. Gallager derived the exact asymptotics (that is, a bound with asymptotically vanishing relative error) of the error probability ...

The fixed effects estimator of panel models can be severely biased because of the well-known incidental parameter problems. It is shown that such bias can be reduced as T grows with n. We consider asymptotics where n and T grow at the same rate as an approximation that allows us to compare bias properties. Under these asymptotics the bias corrected estimators are centered at the truth, whereas ...

We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint distribution of the number of connected components, of the sizes of the giant components, and of the numbers of the excess edges of the giant components. For the sup...

There are several existing ways in developing the asymptotics of the Painlevé transcendents. But it is always a hard task to justify the existence of these asymptotics. In this note, we apply the successive approximation to the general fifth Painlevé equation and rigorously prove the existence of a group of asymptotics of its solutions. 1. Introduction. The mathematical and physical significanc...

Long time asymptotics for some dynamical noise free non-linear filtering problems, new cases. Long time asymptotics for some dynamical noise free non-linear ltering problems, new cases.