Keywords: Law of the logarithm Mixing sequences Precise asymptotics Strong approximation Stationary a b s t r a c t In a recent paper by Spătaru [Precise asymptotics for a series of T. a precise asymptotics in the law of the logarithm for sequence of i.i.d. random variables has been established. In this paper we show that there is an analogous result for strictly stationary ϕ-mixing sequence. T...

Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced vertices with permutation-invariant couplings the asymptotics is non-Weyl only in case of Kirchhoff or anti-Kirchhoff conditions. For graphs with...

Infinitesimal robustness employs first order asymptotics to derive results on uniform (weak) convergence on shrinking neighborhoods around an ideal central model. In the case of the median in the one–dimensional location setup, we refine such a result concerning the convergence of the MSE, proceeding to higher order asymptotics — up to order 1/n , for sample size n . In contrast to usual higher...

This is a continuation of the paper [4] of Bleher and Fokin, in which the large n asymptotics is obtained for the partition function Zn of the six-vertex model with domain wall boundary conditions in the disordered phase. In the present paper we obtain the large n asymptotics of Zn in the ferroelectric phase. We prove that for any ε > 0, as n → ∞, Zn = CG nFn 2 [1+O(e−n 1−ε )], and we find the ...

In this article we present a new method of Rossby asymptotics for the equations of the atmosphere similar to the geostrophic asymptotics. We depart from the classical geostrophics (see J. G. Charney [5] and our previous article [29]) by considering an asymptotics valid for the whole atmosphere, not only in midlatitude regions, and by taking into account the spherical form of the earth. We obtai...

We consider the classical M/G/1 queue with two priority classes and the nonpreemptive and preemptive-resume disciplines. We show that the low-priority steady-state waiting-time can be expressed as a geometric random sum of i.i.d. random variables, just like the M/G/1 FIFO waiting-time distribution. We exploit this structures to determine the asymptotic behavior of the tail probabilities. Unlike...

We consider a class of ergodic Hamilton-Jacobi-Bellman (HJB) equations, related to large time asymptotics of non-smooth multiplicative functional of diffusion processes. Under suitable ergodicity assumptions on the underlying diffusion, we show existence of these asymptotics, and that they solve the related HJB equation in the viscosity sense.

We offer fairly simple and direct proofs of the asymptotics for the scaled Kramers-Smoluchowski equation in both one and higher dimensions. For the latter, we invoke the sharp asymptotic capacity asymptotics of Bovier–Eckhoff–Gayrard–Klein [B-E-G-K].

Let {X(t) : t ∈ [0,∞)} be a centered Gaussian process with stationary increments and variance function σ X(t). We study the exact asymptotics of P(supt∈[0,T ] X(t) > u), as u → ∞, where T is an independent of {X(t)} nonnegative Weibullian random variable. As an illustration we work out the asymptotics of supremum distribution of fractional Laplace motion.

We approximate the Bolker-Pacala model of population dynamics with the logistic Markov chain and analyze the latter. We find the asymptotics of the degenerated hypergeometric function and use these to prove a local CLT and large deviations result. We also state global limit theorems and obtain asymptotics for the first passage time to the boundary of a large interval.