Superprocess information

An $(\xi ,d,\beta )$ -superprocess, $X(t,dx)$ , within mathematics probability theory is a stochastic process on $\mathbb {R} \times \mathbb {R} ^{d}$ 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 $\mathbb {R}$ .

Superprocess information

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Superprocess

Brownian snake

Autoregressive model

Diffusion process

Gaussian random field

SABR volatility model

Branching process