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.

Using machine vision classification to control access of animals to water

Invasive vertebrate pests together with overabundant native species cause significant economic and environmental damage in the Australian rangelands. Access to artificial watering points, created for the pastoral industry, has been a major factor in the spread and survival of these pests. Existing methods of controlling watering points are mechanical and cannot discriminate between target species. This paper describes an intelligent system of controlling watering points based on machine vision technology. Initial test results clearly demonstrate proof of concept for machine vision in this application. These initial experiments were carried out as part of a 3-year project using machine vision software to manage all large vertebrates in the Australian rangelands. Concurrent work is testing the use of automated gates and innovative laneway and enclosure design. The system will have application in any habitat throughout the world where a resource is limited and can be enclosed for the management of livestock or wildlife.