This paper provides a an introduction to some basic properties of Brownian motion. In particular, it shows that Brownian motion exists, that Brownian motion is nowhere differentiability, and that Brownian motion has finite quadratic variation.

We define weighted fractional Brownian sheets, which are a class of Gaussian random fields with four parameters that include fractional Brownian sheets as special cases, and we give some of their properties. We show that for certain values of the parameters the weighted fractional Brownian sheets are obtained as limits in law of occupation time fluctuations of a stochastic particle model. In co...

An 'oscillating' version of Brownian motion is defined and studied. 'Ordinary' Brownian motion and 'reflecting' Brownian motion are shown to arise as special cases. Transition densities, first-passage time distributions, and occupation time distributions for the process are obtained explicitly. Convergence of a simple oscillating random walk to an oscillating Brownian motion process is establis...

This study sought to identify critical areas for puma (Puma concolor) movement across the state of Arizona in the American Southwest and to identify those most likely to be impacted by current and future human land uses, particularly expanding urban development and associated increases in traffic volume. Human populations in this region are expanding rapidly, with the potential for urban center...

Remodeling of the extracellular matrix catalyzed by MMPs is central to morphogenetic phenomena during development and wound healing as well as in numerous pathologic conditions such as fibrosis and cancer. We have previously demonstrated that secreted MMP-2 is tethered to the cell surface and activated by MT1-MMP/TIMP-2-dependent mechanism. The resulting cell-surface collagenolytic complex (MT1...

Abstract Alzheimer’s is a cognitive neurodegenerative disease that mainly affects older adults. Its detection generally evident when the in medium-advanced state of development. The studies are carried out with greater emphasis on part brain, however under scientific evidence there direct relationship psychophysiological measures. Identifying variable can presence this type dementia purpose stu...

Criterion-based segmentation is the problem of subdividing a trajectory into a small number of parts such that each part satisfies a global criterion. We present an algorithmic framework for criterion-based segmentation of trajectories that can efficiently process a large class of criteria. Our framework can handle criteria that are stable, in the sense that these do not change their validity a...

Motivated by the empirical evidence of the long-range dependency found within the Greek motor insurance market, we formulate a particular stochastic pricing model in a continuous framework. We assume the structure of a competitive insurance market where the business volume of each company is directly related to the existing relativity between the company’s premium and the market’s average premi...