Linear di¬usion is an established model for spatial spread in biological systems, including movement of cell populations. However, for interacting, closely packed cell populations, simple di¬usion is inappropriate, because di¬erent cell populations will not move through one another: rather, a cell will stop moving when it encounters another cell. In this paper, I introduce a nonlinear di¬usion ...

Abstract. In this paper we study the pathwise stochastic Taylor expansion, in the sense of our previous work [3], for a class of Itô-type random fields in which the di↵usion part is allowed to contain both the random field itself and its spatial derivatives. Random fields of such an “self-exciting” type particularly contains the fully nonlinear stochastic PDEs of curvature driven di↵usion, as w...

Stable nite di erence approximations of convection-di usion equations lead to large sparse linear systems of equations whose coe cient matrix is an M{matrix, which is highly non symmetric when the convection dominates. For an e cient iterative solution of such systems, it is proposed to consider in the non symmetric case an algebraic multilevel preconditioning method formerly proposed for pure ...

We derive hydrodynamic equations for systems not in local thermodynamic equilibrium, that is, where the local stationary measures are \non-Gibbsian" and do not satisfy detailed balance with respect to the microscopic dynamics. As a main example we consider the driven di usive systems(DDS), such as electrical conductors in an applied eld with di usion of charge carriers. In such systems, the hyd...

The objective of this paper is to model short term interest rate data. Three problems are studied in this paper. First, if we assume that short term interest rates are discrete-time observations of a di usion process, which discretization methods are preferable for parameter estimation and prediction? Second, can we accept the assumption that the short term interest rates are from a discretely ...

This paper studies the problem of diiusion in Markovian models, such as hidden Markov models (HMMs) and how it makes very diicult the task of learning of long-term dependencies in sequences. Using results from Markov chain theory, we show that the problem of diiusion is reduced if the transition probabilities approach 0 or 1. Under this condition, standard HMMs have very limited modeling capabi...

A model is developed for the ow of a slightly compressible uid through a saturated inelastic porous medium. The initial-boundary-value problem is a system that consists of the di usion equation for the uid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto-visco-plastic type. The variational form of this...

We study two modi…cations of the standard model of repeated games with public signals. In one modi…cation, players osberve an underlying public signal at random and privately known times, where the public signals are Poisson events and either the observations occur within a small epsilon time interval or the obsevations have an exponential waiting times. In the second modi…cation, the players o...

We consider a reaction–di usion equation in a bounded domain O⊂Rd, driven by a space– time white noise, with a drift term having polynomial growth and a di usion term which is not boundedly invertible, in general. We are showing that the transition semigroup corresponding to the equation has a regularizing e ect. More precisely, we show that it maps bounded and Borel functions de ned in the Hil...