Spreading rumours in Euclidean space

Abstract

This paper considers the process of spreading rumours in Euclidean space. The rumour (or epidemic) process under study includes (i) a discrete-time stochastic arrival process of new spatially distributed rumours and (ii) a stochastic process of linear transformations of the current rumours which allows for modelling mobility as well as dispersion of rumours. Inspired by linear filtering theory, an affine stochastic recursion in characteristic-function space is studied and numerical transform inversion is used to study the distribution of rumours in space.