Stochastic particle approximations for Smoluchowski's coagulation equation
- Eibeck, Andreas
- Wagner, Wolfgang
2010 Mathematics Subject Classification
- 60K40 65C35
- Stochastic particle method, coagulation equation, variance reduction, gelation phenomena
This paper studies stochastic particle approximations for Smoluchowski's coagulation equation. A new stochastic algorithm with reduced variance is proposed. Its convergence behaviour is investigated, when the number of simulation particles tends to infinity. Under appropriate assumptions on the coagulation kernel, the limit is the unique solution of the coagulation equation. Then detailed numerical experiments are performed, testing the applicability and efficiency of the algorithm. In particular, the gelation phenomenon (loss of mass in the coagulation equation) is studied numerically for several kernels. A striking feature of the new algorithm is a better convergence after the gelation point, providing a tool for detecting the mass of the gel.
- Ann. Appl. Probab. 11 (2001), pp. 1137-1165