Extinction criterion
Theorem taught in Galton–Watson branching, part of Stochastic processes
Extinction criterion
| Type | Theorem |
| Taught in | Galton–Watson branching |
| Part | Stochastic processes |
For a non-degenerate Galton–Watson process with p_0>0, the extinction probability is q=1 when m\le 1, and q<1 when m>1. If p_0=0, extinction is impossible and q=0. The deterministic law \xi\equiv 1 has mean m=1 and extinction probability q=0.
Used in
- Taught in Galton–Watson branching, where the derivation and examples are.
- All 3 questions on Galton–Watson branching