We consider the parameter estimation problem for the scalar di usion type process described by the stochastic equation with time delay

We consider the parameter estimation problem for the scalar di usion type process described by the stochastic equation with time delay

The paper estimates the speed of convergence of the Euler approximation for di usion processes with jump component which have H older continuous coe cients.

A di¤usion walk in Z2 is a (random) walk with unit step vectors !, ", , and #. Particles from di¤erent sources with opposite charges cancel each other when they meet in the lattice. This cancellation principle is applied to enumerate di¤usion walks in shifted half-planes, quadrants, and octants (a 3-D version is also considered). Summing over time we calculate expected numbers of visits and …rs...

Several simple mathematical models for the turbulent di!usion of a passive scalar "eld are developed here with an emphasis on the symbiotic interaction between rigorous mathematical theory (including exact solutions), physical intuition, and numerical simulations. The homogenization theory for periodic velocity "elds and random velocity "elds with short-range correlations is presented and utili...

Scale invariance, either in space or in time, has been shown in many papers to characterize earthquake distributions. Unfortunately, only little work has been dedicated to looking at the general space-time scaling invariance of seismicity systems, even though a better understanding of how the two domains (spatial and temporal) link together could help to the development of the stochastic dynami...

One of the central problems in stereo matching and other image registration tasks is the selection of opti mal window sizes for comparing image regions This paper addresses this problem with some novel algo rithms based on iteratively di using support at dif ferent disparity hypotheses and locally controlling the amount of di usion based on the current quality of the disparity estimate It also ...

In this report, we propose a novel and e cient approach for active unsurpervised texture segmentation. First, we show how we can extract a small set of good features for texture segmentation based on the structure tensor and nonlinear di usion. Then, we propose a variational framework that allows to incorporate these features in a level set based unsupervised segmentation process that adaptivel...

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...

We investigate the model dynamics of a test particle which moves between two parallel plates and is re ected at the walls according to some deterministic periodic re ection law. For a particular continuous velocity model, a di usion limit is derived using the Markov partition approach. It is shown that at least for a large class of discrete velocity models such a limit is not possible. Numerica...