A note on the Balanced method

Recently the Balanced method was introduced as a class of quasi-implicit methods for solving stiff stochastic differential equations. We examine asymptotic and mean-square stability for several implementations of the Balanced method and give a generalized result for the mean-square stability region of any Balanced method. We also investigate the optimal implementation of the Balanced method with respect to strong convergence.

A multicultural study of stereotyping in English-speaking countries

Citizens of 9 different English-speaking countries (N = 619) evaluated the average, or typical, citizen of 5 English-speaking countries (Great Britain, Canada, Nigeria, United States, Australia) on 9 pairs of bipolar adjectives. Participants were drawn from Australia, Botswana, Canada, Kenya, Nigeria, South Africa, the United States, Zambia, and Zimbabwe. There were statistically significant similarities in the rankings of the 5 stimulus countries on 8 of the 9 adjective dimensions and a strong convergence of autostereotypes and heterostereotypes on many traits. The results relate to previous stereotyping research and traditional methods of assessing the accuracy of national stereotypes.

Numerical methods for strong solutions of stochastic differential equations: an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.