Superprocess

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An ${\displaystyle (\xi ,d,\beta )}$-superprocess, ${\displaystyle X(t,dx)}$, within mathematics probability theory is a stochastic process on ${\displaystyle \mathbb {R} \times \mathbb {R} ^{d}}$ that is usually constructed as a special limit of near-critical branching diffusions.

Informally, it can be seen as a branching process where each particle splits and dies at infinite rates, and evolves according to a diffusion equation, and we follow the rescaled population of particles, seen as a measure on ${\displaystyle \mathbb {R} }$.