We investigate the asymptotics of Hankel determinants of the form

In spatial modeling the presence of measurement error, or “nugget”, can have a big impact on the sample behavior of the parameter estimates. This article investigates the nugget effect on maximum likelihood estimators for a onedimensional spatial model: Ornstein-Uhlenbeck plus additive white noise. Consistency and asymptotic distributions are obtained under infill asymptotics, in which a compac...

Spectrum of the second-order differential operator with periodic point interactions in L2 R is investigated. Classes of unitary equivalent operators of this type are described. Spectral asymptotics for the whole family of periodic operators are calculated. It is proven that the first several terms in the asymptotics determine the class of equivalent operators uniquely. It is proven that the spe...

We derive the large n asymptotics of zeros of sections of a generic exponential sum. We divide all the zeros of the nth section of the exponential sum into “genuine zeros,” which approach, as n → ∞, the zeros of the exponential sum, and “spurious zeros,” which go to infinity as n → ∞. We show that the spurious zeros, after scaling down by the factor of n, approach a “rosette,” a finite collecti...

This paper overviews some recent developments in panel data asymptotics, concentrating on the nonstationary panel case and gives a new result for models with individual effects. Underlying recent theory are asymptotics for multi-indexed processes in which both indexes may pass to infinity. We review some of the new limit theory that has been developed, show how it can be applied and give a new ...

The idea of reconstructing of geometry of riemannian manifold M from the Brownian motion on M has been productively explored for a long time (see, for instance, expository article of Pinsky [7] and references therein). In [7] different asymptotics of Brownian motion (mean exit time, distribution of exit time from small ball,...) has been produced and it was shown that it is possible to retrieve...

We study the low energy asymptotics of periodic and random Laplace operators on Cayley graphs of amenable, finitely generated groups. For the periodic operator the asymptotics is characterised by the van Hove exponent or zeroth Novikov-Shubin invariant. The random model we consider is given in terms of an adjacency Laplacian on site or edge percolation subgraphs of the Cayley graph. The asympto...

Two analytical methods have been developed for constructing approximate solutions to a nonlocal generalization of the 1D Fisher– Kolmogorov–Petrovskii–Piskunov equation. This equation is of special interest in studying the pattern formation in microbiological populations. In the greater part of the paper, we consider in detail a semiclassical approximation method based on the WKB–Maslov theory ...

The bootstrap, introduced by Efron (1979), merges simulation with formal model-based statistical inference. A statistical model for a sample Xn of size n is a family of distributions {Pθ,n : θ ∈ Θ}. The parameter space Θ is typically metric, possibly infinite-dimensional. The value of θ that identifies the true distribution from which Xn is drawn is unknown. Suppose that θ̂n = θ̂n(Xn) is a consis...