Linear Systems with Values in [0, ∞)^s

Abstract

All the processes considered in previous chapters have the property that each coordinate η(x) can take on only two values. When the set of possible values per site is allowed to be noncompact, new problems and different phenomena occur. The literature contains many types of models in which the set of possible values per site is either the nonnegative integers or the nonnegative real numbers. The oldest and simplest of these is a system of particles which move independently on 5. This process has been modified by adding a speed change interaction and/or by allowing branching. In these cases, η (x) is interpreted as the number of particles at x. In other models, one can view η (x) as being a nonnegative real-valued characteristic of the particle at x, which is updated in some way which involves interactions among the various sites.