SCANNING BROWNIAN PROCESSES

The 'scanning process' Z(t), t is an element of R-k, of the title is a Gaussian random field obtained by associating with Z(t) the value of a set-indexed Brownian motion on the translate t + A(0) of some 'scann ing set' A(0). We study the basic properties of the random field Z rel ating, for example, its continuity and other sample path properties to the geometrical properties of A(0). We ask if the set A(0) determines the scanning process, and investigate when, and how, it is possible t o recover the structure of A(0) from realisations of the sample paths of the random field Z.