Multidimensional second order generalised stochastic processes on locally compact Abelian groups

Abstract

This thesis is concerned with the harmonic analysis of multidimensional generalised stochastic processes on locally compact Abelian groups. A multidimensional generalised stochastic process is a continuous linear operator from a test function space into a space of H-valued random variables, where H is a separable Hilbert space. The remarkable properties and very simple structure of the Feichtinger algebra So(G) make it very suitable as a test function space in this respect. Classical representation theorems for stationary and harmonisable processes on locally compact Abelian groups which have been extended to infinite dimensions can be proved in in much more compact way, avoiding much of the technical machinery associated with operator valued integration and the theory of operator valued bimeasures.