Nonlinear Processes Associated with the Discrete Smoluchowski Coagulation-Fragmentation Equation,
2003, v.9, №1, 103-130
This paper is dedicated to the probabilistic interpretation of the mass-flow equation which is associated with the discrete Smoluchowski coagulation-fragmentation equation. The mass-flow equation describes the evolution in time of the distribution of the mass with respect to the size of the clusters when the expected numbers of clusters follow Smoluchowski's equation. Under various assumptions on the coagulation and the fragmentation kernels, we construct nonlinear processes linked with the mass-flow equation: the time-marginals of their law solve this equation. When possible, we approximate these processes using simulable interacting particle systems. We deduce by a coupling argument a new uniqueness result concerning the discrete Smoluchowski coagulation-fragmentation equation.
Keywords: coagulation-fragmentation equation,nonlinear jumpprocesses,stochastic interacting particle systems