We study a singular di$usion on Euclidean space which is characterized by the solution of a classical Itô stochastic di$erential equation in which the di$usion coe2cient is not necessarily of full rank. Our motivation is in earlier results of Basak (J. Multivariate Anal. 39 (1991) 44) and Basak and Bhattacharya (Ann. Probab. 20 (1992) 312), who establish su2cient conditions for singular di$usio...

Up owing salty groundwater, evaporating completely at the ground surface, leads to the buildup of a saline boundary layer, usually with solid salt on the surface. The di usion layer below the surface, if stable, may grow to a nite thickness at equilibrium between the up owing salt and downward di usion. Because of the di erent densities of the uids (low fresh water density in the deeper undergr...

This paper develops a Multivariate Weighted Nonlinear Least Square estimator for a jumpdi usion interest rate model (hereafter MWNLS-JD), which also admits a closed form solution to bond price under an equilibrium martingale pricing theorem. The instantaneous interest rate is modeled as a mixture of a continuous square-root di usion and a discrete Poisson jump process, with the jump sizes unifo...

In this paper, a digital halftoning method is proposed to di use error with a more symmetric error distribution by making use of the concept of multiscale error di usion. It can improve the di usion performance by e ectively reducing directional hysteresis. The di usion is roworiented rather than frame-oriented and hence can reduce the latency and a lot of computation e ort as compared with con...

Convergence of stochastic processes with jumps to di!usion processes is investigated in the case when the limit process has discontinuous coe$cients. An example is given in which the diffusion approximation of a queueing model yields a di!usion process with discontinuous di!usion and drift coe$cients. c © 2002 Elsevier Science B.V. All rights reserved. MSC: 60B10; 60K25

Flame sheet problems are on the natural route to the numerical solution of detailed chemistry, laminar di usion ames, which, in turn, are important in many engineering applications. In order to model the ame structure more accurately, we use the vorticity-velocity formulation of the uid ow equations instead of the more traditional stream function-vorticity approach. The numerical solution of th...

We propose a multilevel preconditioning strategy for the iterative solution of large sparse linear systems arising from a nite element discretization of the radiation di usion equations. In particular, these equations are solved using a mixed nite element scheme in order to make the discretization discontinuous, which is imposed by the application in which the di usion equation will be embedded...

In this article, we propose a generalization of the theory of di usion approximation for random ODE to a nonlinear system of random Schrödinger equations. This system arises in the study of pulse propagation in randomly birefringent optical bers. We rst show existence and uniqueness of solutions for the random PDE and the limiting equation. We follow the work of Garnier-Marty [16, 20], where a ...

We consider the parameter estimation problem for the scalar di usion type process described by the stochastic equation with time delay

We consider the parameter estimation problem for the scalar di usion type process described by the stochastic equation with time delay