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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. An ( ,d, )-superprocess, X(t,dx), is a stochastic process on mathbb{R} times mathbb{R}^d 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 -symmetric stable process with infinitesimal generator .The = 2 case corresponds to standard Brownian motion and the (2,d,1)-superprocess is called the Dawson-Watanabe superprocess or super-Brownian motion.