Spatial—temporal marked point processes: a spectrum of stochastic models

✍ Scribed by Eric Renshaw

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 281 KB
• Volume: 21
• Category: Article
• ISSN: 1180-4009
• DOI: 10.1002/env.1019

✦ Synopsis

Abstract

Many processes that develop through space and time do so in response not only to their own individual growth mechanisms but also in response to interactive pressures induced by their neighbours. The growth of trees in a forest which compete for light and nutrient resources, for example, provides a classic illustration of this general spatial—temporal growth‐interaction process. Not only has its mathematical representation proved to be a powerful tool in the study and analysis of marked point patterns since it may easily be simulated, but it has also been shown to be highly flexible in terms of its application since it is robust with respect to incorrect choice of model selection. Moreover, it is highly amenable to maximum likelihood and least squares parameter estimation techniques. Currently the algorithm comprises deterministic growth and interaction coupled with a stochastic arrival and departure mechanism. So for systems with a fixed number of particles there is an inherent lack of randomness. A variety of different stochastic approaches are therefore presented, from the exact event—time model through to the associated stochastic differential equation, taking in time‐increment and Tau‐ and Langevin‐Leaping approximations en route. The main algorithm is illustrated through application to forest management and high‐intensity packing of hard particle systems, and comparisons are made with the established force biased approach. Copyright © 2009 John Wiley & Sons, Ltd.