What is "superprocess"

n. (context mathematics English) A form of stochastic process related to diffusion

An (α, d, β)-superprocess, X(t, dx), is a stochastic process on R × R that is usually constructed as a special limit of branching diffusion where the branching mechanism is given by its factorial moment generating function:

$$\Phi(s) = \frac{1}{1+\beta}(1-s)^{1+\beta}+s$$
and the spatial motion of individual particles is given by the α-symmetric stable process with infinitesimal generator Δ.

The α = 2 case corresponds to standard Brownian motion and the (2, d, 1)-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

Δu − u = 0 on R.