Numerical schemes for advection-di usion problems are often used with non-uniform grids. Non-uniform grids are known to greatly complicate the convergence analysis and their use therefore is much less straightforward than for uniform grids. For example, it is possible that a scheme which is inconsistent at the level of the local truncation error truly converges with order two. The purpose of th...

We design a general mathematical framework to analyze the properties of nearest neighbor balancing algorithms of the di usion type. Within this framework we develop a new optimal polynomial scheme (OPS) which we show to terminate within a nite number m of steps, where m only depends on the graph and not on the initial load distribution. We show that all existing di usion load balancing algorith...

In this paper we present a two-step boundary detection algorithm. The "rst step is a nonlinear smoothing algorithm which is based on an orientation-sensitive probability measure. By incorporating geometrical constraints through the coupling structure, we obtain a robust nonlinear smoothing algorithm, where many nonlinear algorithms can be derived as special cases. Even when noise is substantial...

Nonparametric methods are becoming popular recently in estimating continuous-time di¤usion models due to their ‡exibility. This paper provides a new approach to constructing point-wise con…dence intervals for nonparametric drift and di¤usion functions via empirical likelihood (EL) in conjunction with local linear smoothing. It serves as a promising competitor to the conventional asymptotic norm...

We examine Schweizer's (1991) locally risk-minimizing (LRM) hedge approach for hedging a European call in the case when the stock price follows a Poisson jump di usion process with lognormally distributed jump sizes. In contrast to Merton's (1976) hedging strategy where di usion risk is perfectly hedged while jump risk remains un-hedged, the locally risk-minimizing strategy hedges both di usion...

A di usion model of the roundtrip time experienced by packets on the Internet is developed. The parameters of the di usion system are modeled as Markov processes. The transition probabilities of the parameters are modeled with a mixture of Laplace distributions. The stationary distributions of the parameters are modeled as Normal distributions. The results show that the model is able to reprodu...

This paper provides a review of a new method of addressing problems in di usion Monte Carlo: the Green's function rst-passage method (GFFP). In particular, we address four new strands of thought and their interaction with the GFFP method: the use of angle-averaging methods to reduce vector or tensor Laplace equations to scalar Laplace equations; the use of the simulation-tabulation (ST) method ...

We describe the use of upwind monotonic interpolation methods for the solution of the time-dependent radiative transfer equation in both optically thin and thick media. These methods, originally developed to solve Eulerian advection problems in hydrodynamics, have the ability to propagate sharp features in the ow with very little numerical di usion. We consider the implementation of both explic...

The segmentation of structure from images is an inherently di cult problem in computer vision and a bottleneck to its widespread application, e.g., in medical imaging. This paper presents an approach for integrating local evidence such as regional homogeneity and edge response to form global structure for gure-ground segmentation. This approach is motivated by a shock-based morphogenetic langua...