In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale difference sequences or stationary sequences satisfying projective criteria. Applications to functions of linear processes and to functions of expanding maps of the interval are given.

We present an analysis of the mean-field kinetics of Brownian coagulation of droplets and polymers driven by input of monomers which aims to characterize the long time behavior of the cluster size distribution as a function of the inverse fractal dimension, a, of the aggregates. We find that two types of long time behavior are possible. For 0≤a<1/2 the size distribution reaches a stationary sta...

Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. The limiting stationary distribution of the Markov chain represents the fraction of the time spent in each state during the stochastic process. A standard way to compute this distribution for a random walk on a finite set of states is to compute the Perron vector of the associated transition ...

Rolled stationary phases are fabrics (i.e., nonparticulate phases) that rapidly separate proteins from salts on the basis of size exclusion. Pore size and pore size distributions in the stationary phase determine how different size molecules distribute between the stationary and mobile phases in liquid chromatography columns. The potential for size exclusion chromatography by fabrics is not ini...

A novel thresholding algorithm for change detection in video sequences is proposed. The method is based on image differencing and the intensity distribution of a difference image. With a difference image between two consecutive images, we prepare a new image model for the distribution of stationary pixels. The distribution of moving pixels is then separated by extracting the distribution of sta...

We construct a stochastic fluid process with an underlying piecewise deterministic Markov (PDMP) akin to the one used in construction of rational arrival (RAP) Asmussen and Bladt (1999) which we call RAP-modulated process. As opposed classic Markov-modulated driven by jump process, PDMP has continuous state space is matrix parameters may not be related intensity matrix. Through novel techniques...