Derivation of continuous equations for density of burglars

Abstract

The discrete model for movement of burglars is given by the equation as: where R(x, t) is assumed to be strictly positive across the whole spatial domain for all t.We can express the relation in terms of discrete spatial laplacian . For this, in continuous limit, we re-express p(x, t) in terms of p(x, t) and R(x, t) R(X, t), p(x, t) p(X, t), where X=lx, l, is a grid spacing