Markov Point Processes and Their Applications

The splitting extrapolation method is a newly developed technique for solving multidimensional mathematical problems. It overcomes the difficulties arising from Richardson's extrapolation when applied to these problems and obtains higher accuracy solutions with lower cost and a high degree of parallelism. The method is particularly suitable for solving large scale scientific and engineering problems. This book presents applications of the method to multidimensional integration, integral equations and partial differential equations. It also gives an introduction to combination methods which are relevant to splitting extrapolation. The book is intended for those who may exploit these methods and it requires only a basic knowledge of numerical analysis Part 1 Point processes: the Poisson process; finite point processes; interior and exterior conditioning. Part 2 Markov point processes: Ripley-Kelly Markov point processes; marked point processes; nearest-neighbour Markov point processes. Part 3 Statistics for Markov point processes: simulation; parameter estimation. Part 4 Applications: modelling of spatial patterns; higher-level vision