In this paper we investigate a family of partial di erential equations (PDEs) for image processing which can be regarded as isotropic nonlinear di usion with an additional factor on the right-hand side. The one-dimensional analogues to this lter class have been motivated as scaling limits of one-dimensional adaptive averaging schemes. In 2-D, mean curvature motion is one of the most prominent e...

The stochastic analysis is presented for the parameter estimation problem for tting a theoretical jump-di usion model to the log-returns from closing data of the Standard and Poor's 500 (S&P500) stock index during the prior decade 1992-2001. The jump-di usion model combines a the usual geometric Brownian motion for the di usion and a space-time Poisson process for the jumps such that the jump a...

image restoration has been an active research area. dierent formulations are eective in high qualityrecovery. partial dierential equations (pdes) have become an important tool in image processingand analysis. one of the earliest models based on pdes is perona-malik model that is a kindof anisotropic diusion (andi) lter. anisotropic diusion lter has become a valuable tool indierent elds...

A resolution enhancement scheme is presented. It consists of interpolation followed by processing with an adaptive nonlinear forward-and-backwarddi usion process that enhances edges while suppressing interpolation ringings and denoising smooth areas. keywords: super-resolution, image interpolation, anisotropic di usion, image enhancement, scale-space.

This paper studies the problem of di usion in Markovian models such as hidden Markov models HMMs and how it makes very di cult the task of learning of long termdependencies in sequences Using results from Markov chain theory we show that the problem of di usion is reduced if the transition probabilities approach or Under this condition standard HMMs have very limited modeling capabilities but i...

The aim of this paper is to investigate the mathematical properties of a continuum model for di usion of multiple species incorporating size exclusion e ects. The system for two species leads to nonlinear cross-di usion terms with double degeneracy, which creates signi cant novel challenges in the analysis of the system. We prove global existence of weak solutions and well-posedness of strong s...

In this paper we prove the convergence of a nite volume scheme to the solution of a Stefan problem, namely the nonlinear diiusion equation ut ?'(u) = v, together with a homogeneous Neumann boundary condition and an initial condition. This is done by means of a priori estimates in L 1 and use of Kolmogorov's theorem on relative compactness of subsets of L 2 .

it is known that a stochastic dierential equation (sde) induces two probabilisticobjects, namely a diusion process and a stochastic ow. while the diusion process isdetermined by the innitesimal mean and variance given by the coecients of the sde,this is not the case for the stochastic ow induced by the sde. in order to characterize thestochastic ow uniquely the innitesimal covariance give...

Transport theory's equation of transfer is a well-accepted model for wave scattering in a random medium. However, exact solutions are only available for a small class of special cases (isotropic scattering in in nite and semiin nite domains) and thus, analytic solutions for a wide variety of geometries and range of parameters which correspond to more physically relevant situations still remain ...

This paper deals with development and analysis of a fully discrete nite element method for a nonlinear di erential system for describing an air water system in groundwater hydrol ogy The nonlinear system is written in a fractional ow formulation i e in terms of a saturation and a global pressure The saturation equation is approximated by a nite element method while the pressure equation is trea...