Stochastic spatial processes

Abstract

In this section some basic concepts and theorems in the theory of stochastic processes in two dimensions are reviewed (For details see Bartlett, 1966; Whittle 1954; Ripley, 1981). In particular we are interested to give a formal description of processes that may be thought as underlying a geographical distribution of an economic variable. This is the main concern of the whole book. The most general situation in regional economics is to have to cope with data recorded in irregular collecting areas such as counties, regions or states. (Haggett, Cliff and Frey 1964, p.349). For this reason, when we speak of sites, we often have in mind portions of space rather than points, and when we say set of sites we normally think of irregular rather then regular lattices. Furthermore most of the economic variables are likely to be continuous and therefore the focus will be, throughout the chapter, on continuous processes recorded on a discrete space.