For many time series in empirical macro and finance, it is assumed that the logarithms of the series is a unit root processes. This assumption implies that the level of such a time series is the exponential of a unit root process. Therefore, it is of interest to investigate the behavior of such time series prior to taking their logarithms. This paper shows that the sum of the exponential of a r...

T HE Erlang distribution has been used to model the runway service process in queuing models of air traffic operations [1–3] since its use was first proposed by Hengsbach and Odoni [4]. It has been shown to offer certain computational advantages because it can be viewed as a sum of exponential distributions. However, there have been few prior efforts to validate Erlang distribution assumptions ...

We show there is a residual subset S(M) of Diff1(M) such that, for every f ∈ S(M), any homoclinic class of f containing periodic saddles p and q of indices α and β, respectively, where α < β, has superexponential growth of the number of periodic points inside the homoclinic class. Furthermore, it is shown the super-exponential growth occurs for hyperbolic periodic points of index γ inside the h...

We consider the stabilization of the transmission problem of Naghdi’s model by boundary feedbacks where the model has a middle surface of any shape. The exponential decay rate for the problem is established under some checkable geometric conditions on the middle surface.  2005 Elsevier Inc. All rights reserved.

The aim of this paper is to analyze the connections between the exponential dichotomy of a semigroup on a Banach space X and the admissibility of the pair (`p(N, X), `q(N, X)). We obtain necessary and sufficient conditions for exponential dichotomy of exponentially bounded semigroups using discrete time techniques.

We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.

We analytically calculate the local density of states for Cauchy random band matrices with strongly fluctuating diagonal elements. The Breit-Wigner form for ordinary band matrices is replaced by a Levy distribution of index μ = 1/2 and the characteristic energy scale α is strongly enhanced as compared to the Breit-Wigner width. The unperturbed eigenstates decay according to the non-exponential ...

We construct 2-dimensional CAT(-1) groups which contain free subgroups with arbitrary iterated exponential distortion, and with distortion higher than any iterated exponential.

We consider a classical model related to an empirical distribution function Fn(t) = 1 n Pn k=1 I{ξk≤t} of (ξk)i≥1 – i.i.d. sequence of random variables, supported on the interval [0, 1], with continuous distribution function F (t) = P(ξ1 ≤ t). Applying “Stopping Time Techniques”, we give a proof of Kolmogorov’s exponential bound

In this paper we consider two counting problems associated with compact negatively curved surfaces and improve classical asymptotic estimates due to Margulis. In the first, we show that the number of closed geodesics of length at most T has an exponential error term. In the second we show that the number of geodesic arcs (between two fixed points x and y) of length at most T has an exponential ...