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...

Traditional error di usion halftoning is a high quality method for producing 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 p...

The aim of this paper is to discuss di erent couplings between di usion, recrystallisation/grain growth, strain/stress, heat transfer and thermo-mechanical behaviour of metallic materials. The understanding of these di erent physical phenomena is needed to predict the long-term life of mechanical parts in components. Some results are presented and further studies are suggested to improve the ev...

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...

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...

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...

ARPA Image Understanding Workshop 1996 As an alternative to texture segmentation for the description of the images, we propose a method for coalescing descriptors of adjacent image patches with similar textural content into tight clusters. We achieve this result by extending the notion of edge-preserving smoothing and anisotropic di usion from gray-level and color images to vector-valued images...

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

We derive a two-scale homogenization limit for reaction-di usion systems where for some species the di usion length is of order 1 whereas for the other species the di usion length is of the order of the periodic microstructure. Thus, in the limit the latter species will display di usion only on the microscale but not on the macroscale. Because of this missing compactness, the nonlinear coupling...

In this work we introduce a new class of lowest order methods for di usive problems on general meshes with only one unknown per element. The underlying idea is to construct an incomplete piecewise a ne polynomial space with su cient approximation properties starting from values at cell centers. To do so we borrow ideas from multi-point nite volume methods, although we use them in a rather di er...