We study the concept of quadratic variation a continuous path along sequence partitions and its dependence with respect to choice partition sequence. introduce roughness show that for Hölder-continuous paths satisfying this condition, balanced is invariant Typical Brownian motion are shown satisfy property almost-surely any required step size condition. Using these results we derive formulation...

Richardson Extrapolation is a powerful computational tool which can successfully be used in the efforts to improve the accuracy of the approximate solutions of systems of ordinary differential equations (ODEs) obtained by different numerical methods (including here combined numerical methods consisting of appropriately chosen splitting procedures and classical numerical methods). Some stability...

in this paper, we study the problem of minimizing the ratio of two quadratic functions subject to a quadratic constraint. first we introduce a parametric equivalent of the problem. then a bisection and a generalized newton-based method algorithms are presented to solve it. in order to solve the quadratically constrained quadratic minimization problem within both algorithms, a semidefinite optim...

People can estimate the current position of an occluded moving target. This is called motion extrapolation, and it has been suggested that the performance in such tasks is mediated by the smooth-pursuit system. Experiment 1 contrasted a standard position extrapolation task with a novel number extrapolation task. In the position extrapolation task, participants saw a horizontally moving target b...