In this paper, we are interested in the one-dimensional porous medium equation when the initial condition is the distribution function of a probability measure. We associate a nonlinear martingale problem with it. After proving uniqueness for the martingale problem, we show existence owing to a propagation of chaos result for a system of weakly interacting di usion processes. The particle syste...

I develop an omnibus speci…cation test for di¤usion models based on the in…nitesimal operator instead of the already extensively used transition density. The in…nitesimal operatorbased identi…cation of the di¤usion process is equivalent to a "martingale hypothesis" for the new processes transformed from the original di¤usion process. The transformation is via the celebrated "martingale problems...

This appendix shows simulation results using URDME and MesoRD for a simple di↵usion problem. This problem illustrates the advantage of unstructured meshes: the ability to resolve processes on curved surfaces without causing a unnecessarily fine discretization. We also evaluate the accuracy of the software on a non-trivial reaction-di↵usion system by simulating the example of Min oscillations pr...

We develop a new framework to calibrate stochastic volatility option pricing models to an arbitrary prescribed set of prices of liquidly traded options. Our approach produces an arbitrage-free stochastic volatility di usion process that minimizes the distance to a prior di usion model. We use the notion of relative entropy (also known under the name of Kullback-Leibler distance) to quantify the...

Adaptive Finite Element Simulation of Currents at Mi roele trodes to a Guaranteed A ura y. Appli ation to Channel Mi roband Ele trodes. Kathryn Harriman David Gavaghan Paul Houston David Kay Endre S uli We extend our earlier work (see K. Harriman et al., Te hni al Report NA99/19) on adaptive nite element methods for dis ele trodes to the ase of rea tion me hanisms to the in reasingly popular h...

We present a semi discrete method for constructing approximate solutions to the initial value problem for the m dimensional convection di usion equation ut r f u u The method is based on the use of operator splitting to isolate the convection part and the di usion part of the equation In the casem dimensional splitting is used to reduce the m dimensional convection problem to a series of one di...

Traditional error di usion halftoning produces high quality binary images from digital grayscale images. Error di usion shapes the quantization noise power into the high frequency regions where the human eye is the least sensitive. Error di usion may be extended to color images by using error lters with matrix-valued coe cients to take into account the correlation among color planes. We propose...

One of the central problems in stereo matching (and other image registration tasks) is the selection of optimal window sizes for comparing image regions. This paper addresses this problem with some novel algorithms based on iteratively di using support at di erent disparity hypotheses, and locally controlling the amount of di usion based on the current quality of the disparity estimate. It also...

We derive a fractional reaction–di usion equation from a continuous-time random walk model with temporal memory and sources. The equation provides a general model for reaction–di usion phenomena with anomalous di usion such as occurs in spatially inhomogeneous environments. As a rst investigation of this equation we consider the special case of single species fractional reaction–di usion in one...

Conventional grayscale error di usion halftoning produces worms and other objectionable artifacts. Tone Dependent error di usion for grayscale halftoning (Li and Allebach) helps reduce these artifacts by controlling di usion of quantization errors based on the input graylevel value. Allebach et al. design error lters weights and thresholds for each (input) graylevel optimized based on a human v...