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An -superprocess, , is a stochastic process on that is usually constructed as a special limit of branching diffusion where the branching mechanism is given by its factorial moment generating function:

and the spatial motion of individual particles is given by the -symmetric stable process with infinitesimal generator .

The case corresponds to standard Brownian motion and the -superprocess is called the Dawson-Watanabe superprocess or super-Brownian motion.

One of the most important properties of superprocesses is that they are intimately connected with certain nonlinear partial differential equations. The simplest such equation is


  • Eugene B. Dynkin (2004). Superdiffusions and positive solutions of nonlinear partial differential equations. Appendix A by J.-F. Le Gall and Appendix B by I. E. Verbitsky. University Lecture Series, 34. American Mathematical Society. ISBN 9780821836828. 
  • Alison Etheridge (2000). An Introduction to Superprocesses. American Mathematical Society. ISBN 9780821827062.