Exact simulation of nonlinear coagulation processes

Abstract

The Smoluchowski equation is a nonlinear integro-differential equation describing the evolution of the concentration μ t ( dx ) of particles of mass in ( x , x + dx ) in an infinite particle system where coalescence occurs. We introduce a class of algorithms, which allow, under some conditions, to simulate exactly a stochastic process ( X t ) t ≥0 , whose time marginals are given by ( xμ t ( dx )) t ≥0 .