Asymptotic analysis of the Gunn effect with realistic boundary conditions

A general asymptotic analysis of the Gunn effect in n-type GaAs under general boundary conditions for metal-semiconductor contacts is presented. Depending on the parameter values in the boundary condition of the injecting contact, different types of waves mediate the Gunn effect. The periodic current oscillation typical of the Gunn effect may be caused by moving charge-monopole accumulation or depletion layers, or by low- or high-field charge-dipole solitary waves. A new instability caused by multiple shedding of (low-field) dipole waves is found. In all cases the shape of the current oscillation is described in detail: we show the direct relationship between its major features (maxima, minima, plateaus, etc.) and several critical currents (which depend on the values of the contact parameters). Our results open the possibility of measuring contact parameters from the analysis of the shape of the current oscillation.

On the relationship between connections and the asymptotic properties of predictive distributions

In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributions, using the Kullback-Leibler divergence as a loss function. He showed that estimative distributions with asymptotically efficient estimators can be improved by predictive distributions that do not belong to the model. The model is assumed to be a multidimensional curved exponential family. In this paper we generalize the result assuming as a loss function any f divergence. A relationship arises between alpha connections and optimal predictive distributions. In particular, using an alpha divergence to measure the goodness of a predictive distribution, the optimal shift of the estimate distribution is related to alpha-covariant derivatives. The expression that we obtain for the asymptotic risk is also useful to study the higher-order asymptotic properties of an estimator, in the mentioned class of loss functions.

On an asymptotic formula for the maximum voltage drop in a on-chip power distribution network

We present a new asymptotic formula for the maximum static voltage in a simplified model for on-chip power distribution networks of array bonded integrated circuits. In this model the voltage is the solution of a Poisson equation in an infinite planar domain whose boundary is an array of circular pads of radius ", and we deal with the singular limit Ɛ → 0 case. In comparison with approximations that appear in the electronic engineering literature, our formula is more complete since we have obtained terms up to order Ɛ15. A procedure will be presented to compute all the successive terms, which can be interpreted as using multipole solutions of equations involving spatial derivatives of functions. To deduce the formula we use the method of matched asymptotic expansions. Our results are completely analytical and we make an extensive use of special functions and of the Gauss constant G

Capacity of MIMO Channels: asymptotic evaluation under correlated fading

This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multiple-inputmultiple-output channels with fading correlation at either thetransmitter or the receiver. We consider the asymptotic situation,where the number of inputs and outputs increase without boundat the same rate. A simple uniparametric model for the fadingcorrelation function is proposed and the asymptotic capacity perantenna is derived in closed form. Although the proposed correlationmodel is introduced only for mathematical convenience, itis shown that its shape is very close to an exponentially decayingcorrelation function. The asymptotic expression obtained providesa simple and yet useful way of relating the actual fadingcorrelation to the asymptotic capacity per antenna from a purelyanalytical point of view. For example, the asymptotic expressionsindicate that fading correlation is more harmful when arising atthe side with less antennas. Moreover, fading correlation does notinfluence the rate of growth of the asymptotic capacity per receiveantenna with high Eb /N0.

Asymptotic equivalence between the unconditional maximum likelihood and the square-law nonlinearity symbol timing estimation

This paper provides a systematic approach to theproblem of nondata aided symbol-timing estimation for linearmodulations. The study is performed under the unconditionalmaximum likelihood framework where the carrier-frequencyerror is included as a nuisance parameter in the mathematicalderivation. The second-order moments of the received signal arefound to be the sufficient statistics for the problem at hand and theyallow the provision of a robust performance in the presence of acarrier-frequency error uncertainty. We particularly focus on theexploitation of the cyclostationary property of linear modulations.This enables us to derive simple and closed-form symbol-timingestimators which are found to be based on the well-known squaretiming recovery method by Oerder and Meyr. Finally, we generalizethe OM method to the case of linear modulations withoffset formats. In this case, the square-law nonlinearity is foundto provide not only the symbol-timing but also the carrier-phaseerror.

A Sequential Allocation Problem: The Asymptotic Distribution of Resources

In this paper we consider a sequential allocation problem with n individuals. The first individual can consume any amount of some endowment leaving the remaining for the second individual, and so on. Motivated by the limitations associated with the cooperative or non-cooperative solutions we propose a new approach. We establish some axioms that should be satisfied, representativeness, impartiality, etc. The result is a unique asymptotic allocation rule. It is shown for n = 2; 3; 4; and a claim is made for general n. We show that it satisfies a set of desirable properties. Key words: Sequential allocation rule, River sharing problem, Cooperative and non-cooperative games, Dictator and ultimatum games. JEL classification: C79, D63, D74.

Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic models

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin con- volution of functions de ned on (0;1), and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-di usion models and stochastic volatility models with jumps. We apply our general results to the Heston model with double exponential jumps, and make a detailed analysis of the asymptotic behavior of the stock price density, the call option pricing function, and the implied volatility in this model. We also obtain similar results for the Heston model with jumps distributed according to the NIG law.

Stellar population synthesis: the effect of improved Asymptotic Giant Branch models and of interstellar dust on mass-to-light–color relations

Teoreettisen populaatiosynteesin avulla voidaan mallintaa tähtijoukkojen ja galaksien fotometrisiä ominaisuuksia yhdistämällä yksittäisten tähtien tuottama säteily, joka saadaan teoreettisista tähtien kehitysmalleista. Valitsemalla sopiva massajakauma syntyville tähdille voidaan muodostaa yksinkertainen tähtipopulaatio, joka koostuu saman ikäisistä ja kemialliselta koostumukseltaan yhtenäisistä tähdistä. Monimutkaisempia tähtipopulaatioita voidaan muodostaa konvoloimalla yksinkertaisten tähtipopulaatioiden luminositeetti jonkin valitun tähtienmuodostushistorian kanssa sekä yhdistämällä näin muodostettuja populaatioita. Tässä työssä tarkastellaan asymptoottisen jättiläishaaran (AGB) tähtien uusien, tarkentuneiden evoluutiomallien vaikutusta populaatiosynteesin tuloksiin niin yksinkertaisten tähtipopulaatioiden kuin galaksien mallinnukseen soveltuvien monimutkaisempien tähtipopulaatioiden kohdalla. Työn päätarkoitus on tuottaa uudistuneisiin malleihin perustuvat populaation massa-luminositeetti -suhteen ja värin väliset relaatiot (MLC-relaatiot). MLC-relaatioita voidaan käyttää populaation massan määrittämiseen sen fotometristen ominaisuuksien (väri, luminositeetti) perusteella. Lisäksi tutkitaan tähtienvälisen pölyn vaikutusta yksinkertaisen spiraaligalaksimallin MLC-relaatioihin. Työssä käytetyt tähtien kehitysmallit perustuvat julkaisuun Marigo et al. (Astronomy & Astrophysics 482, 2008). Havaitaan, että AGB-tähtien vaikutus populaation integroituun luminositeettiin on pieni näkyvillä aallonpituuksilla, mutta merkittävä lähi-infrapuna-alueella. Vaikutus MLC-relaatioihin on vastaavasti merkittävä tarkkailtaessa luminositeettia lähi-infrapunassa sekä käytettäessä värejä, joissa yhdistetään optisia ja lähi-infrapunan kaistoja. Todetaan, että MLC-relaatioiden käyttö lähi-infrapunassa edellyttää tarkentuneen AGB-vaiheen sisällyttämistä populaatiosynteesin malleihin. Tähtienvälisen pölyn vaikutus MLC-relaatioihin todetaan riippuvan käytetystä kaistasta ja väristä, mutta vaikutuksen havaitaan olevan suurin optisen ja lähi-infrapunan väriyhdistelmillä.

Asymptotic Approximations in the Near-Integrated Model with a Non-Zero Initial Condition

This paper considers various asymptotic approximations in the near-integrated firstorder autoregressive model with a non-zero initial condition. We first extend the work of Knight and Satchell (1993), who considered the random walk case with a zero initial condition, to derive the expansion of the relevant joint moment generating function in this more general framework. We also consider, as alternative approximations, the stochastic expansion of Phillips (1987c) and the continuous time approximation of Perron (1991). We assess how these alternative methods provide or not an adequate approximation to the finite-sample distribution of the least-squares estimator in a first-order autoregressive model. The results show that, when the initial condition is non-zero, Perron's (1991) continuous time approximation performs very well while the others only offer improvements when the initial condition is zero.

Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form

In this paper, we study the asymptotic distribution of a simple two-stage (Hannan-Rissanen-type) linear estimator for stationary invertible vector autoregressive moving average (VARMA) models in the echelon form representation. General conditions for consistency and asymptotic normality are given. A consistent estimator of the asymptotic covariance matrix of the estimator is also provided, so that tests and confidence intervals can easily be constructed.