Starting with theWigner distribution formulation for beam wave propagation in Hölder continuous non-Gaussian random refractive index fields we show that the wave beam regime naturally leads to the white-noise scaling limit and converges to a Gaussian white-noise model which is characterized by the martingale problem associated to a stochastic differential-integral equation of the Itô type. In t...

We consider the estimation of coefficients of a structural equation with many instrumental variables in a simultaneous equation system. It is mathematically equivalent to an estimating equation estimation or a reduced rank regression in the statistical linear models when the number of restrictions or the dimension increases with the sample size. As a semi-parametric method, we propose a class o...

In this note we study the problem of simultaneous stabilization for the algebra AR(D). Invertible pairs (fj , gj), j = 1, . . . , n, in a commutative unital algebra are called simultaneously stabilizable if there exists a pair (α, β) of elements such that αfj + βgj is invertible in this algebra for j = 1, . . . , n. For n = 2, the simultaneous stabilization problem admits a positive solution fo...

  The main purpose of this study is to estimate the maritime transportation elasticities of the environmental pollution and economic growth in Iran within the short-run and long-run to find out the relationships among maritime transportation, environmental pollution and economic growth. The lagged endogenous model (a dynamic log-linear model that we used) is estimated using two distinctive ...

Consider testing the null hypothesis that a single structural equation has specified coefficients. The alternative hypothesis is that the relevant part of the reduced form matrix has proper rank, that is, that the equation is identified. The usual linear model with normal disturbances is invariant with respect to linear transformations of the endogenous and of the exogenous variables. When the ...

Differential equations have been used in statistics to define functions such as probability densities. But the idea of using differential equation formulations of stochastic models has a much wider scope. The author gives several examples, including simultaneous estimation of a regression model and residual density, monotone smoothing, specification of a link function, differential equation mod...

We consider the estimation of the coefficients of a linear structural equation in a simultaneous equation system when there are many instrumental variables. We derive some asymptotic properties of the limited information maximum likelihood (LIML) estimator when the number of instruments is large; some of these results are new as well as old, and we relate them to results in some recent studies....

We study the regularized, oscillatory, multiscale, quasilinear, elliptic problem in divergence form − div(Qη(x, x , u)∇u) = f, in Ω, (0.1) u = g, on ∂Ω, (0.2) assuming that the conductivity has the form Qη(x, y, r) = a−(x) + (a+(x)− a−(x))βη(r − ψ(x, y)), (0.3) for some domain Ω ⊂ Rn, n ≥ 1, a regularization βη of the Heaviside step function and a locally periodic function ψ(x, y), Y -periodic ...