Integro-local theorems for sums of independent random vectors in the series scheme

Let S(n) = ξ(1)+?+ξ(n) be a sum of independent random vectors ξ(i) = ξ _(n)(i) with general distribution depending on a parameter n. We find sufficient conditions for the uniform version of the integro-local Stone theorem to hold for the asymptotics of the probability P(S(n) ∈ Δ[x), where Δ[x) is a cube with edge Δ and vertex at a point x.     

On the Asymptotic Behavior of the Distributions of First-Passage Times, I

In this paper, the asymptotic behavior of and estimates for the distribution of first-passage times for a random walk are obtained in the cases of fixed and increasing levels. In the first part of the paper, the case of zero level is studied.     

Large deviations for random walks with nonidentically distributed jumps having infinite variance

Let = _i = 1^n _i , S_n = _k n S_k

Paramagnetic relaxation of radical cations in alkane solutions as measured by time-resolved magnetic field effects

Spin-lattice relaxation times of radical cations were measured by the decay of the time-resolved magnetic field effect in the recombination fluorescence of radical ion pairs in liquid hydrocarbons at high concentrations of solvent holes acceptor. The dependences of spin-lattice relaxation time on the magnetic field strength and solvent viscosity were studied. The results could not be explained in terms of the model of ion-molecular charge transfer involving monomeric or dimeric radical cations. The paramagnetic relaxation observed in a weak magnetic field is attributed to internal reorganizations of aggregates that originate from radical cations at high acceptor concentration.     

Study of the state of nickel in ion-exchanged NiNaY zeolite by IR spectroscopy using molecular hydrogen adsorbed at low temperatures

The state of nickel cations in NiNaY zeolite subjected to thermal vacuum and oxidative-reductive treatment was analyzed using diffuse reflectance IR spectra of molecular hydrogen, CO, and hydroxy groups. In a sample dehydrated at 570 K, nickel forms oxide particles, which are presumably located in big cavities of a zeolite. Heating of the sample at 670 K results in decomposition of the oxide with the participation of hydroxy groups followed by the formation of stabilized Ni²⁺ cations in large cavities of the zeolite. Calcination of NiNaY zeolite in a hydrogen atmosphere at 730 K leads to Ni²⁺ cation reduction to the metal state and to the formation of acidic hydroxy groups. Nevertheless, Ni²⁺ cations can be regenerated by reoxidation of the reduced sample with oxygen at 670 K and further evacuation at 870 K. Thermal destruction of NiO in the reoxidized sample also proceeds on acidic hydroxy groups, but the temperature of this process is higher than the temperature of oxide decomposition in the initial NiNaY zeolite. The IR spectra of molecular hydrogen complexes with Ni²⁺ cations were observed for the first time. A considerable decrease in the H-H stretching vibration frequency for the coordinated molecules (up to 210 cm’1) can be explained by electron density redistribution between a hydrogen molecule and the cation in the complex     

Asymptotic results on infinite tandem queueing networks

We consider an infinite tandem queueing network consisting of ·/GI/1/∞ stations with i.i.d. service times. We investigate the asymptotic behavior of t(n, k), the inter-arrival times between customers n and n + 1 at station k, and that of w(n, k), the waiting time of customer n at station k. We establish a duality property by which w(n, k) and the “idle times”y(n, k) play symmetrical roles. This duality structure, interesting by itself, is also instrumental in proving some of the ergodic results. We consider two versions of the model: the quadrant and the half-plane. In the quadrant version, the sequences of boundary conditions {w(0,k), k∈ℕ} and {t(n, 0), n∈ℕ}, are given. In the half-plane version, the sequence {t(n, 0), n∈ℕ} is given. Under appropriate assumptions on the boundary conditions and on the services, we obtain ergodic results for both versions of the model. For the quadrant version, we prove the existence of temporally ergodic evolutions and of spatially ergodic ones. Furthermore, the process {t(n, k), n∈ℕ} converges weakly with k to a limiting distribution, which is invariant for the queueing operator. In the more difficult half plane problem, the aim is to obtain evolutions which are both temporally and spatially ergodic. We prove that 1/n∑ _k=1 ⁿ w(0, k) converges almost surely and in L ₁ to a finite constant. This constitutes a first step in trying to prove that {t(n,k), n∈ℤ} converges weakly with k to an invariant limiting distribution. Received: 23 March 1999 / Revised version: 5 January 2000 / Published online: 12 October 2000