Superprocess

An ${\displaystyle (\alpha ,d,\beta )}$-superprocess, ${\displaystyle X(t,dx)}$, is a on ${\displaystyle \mathbb {R} \times \mathbb {R} ^{d}}$ that is usually constructed as a special limit of branching diffusion where the branching mechanism is given by its factorial moment generating function:

and the spatial motion of individual particles is given by the ${\displaystyle \alpha }$-symmetric stable process with infinitesimal generator ${\displaystyle \Delta _{\alpha }}$.

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