Uniqueness of the null solution to a nonlinear partial differential equation satisfied by the explosion probability of a branching diffusion

Uniqueness of the null solution to a nonlinear partial differential equation satisfied by the explosion probability of a branching diffusion

The explosion probability before time t of a branching diffusion satisfies a nonlinear parabolic partial differential equation. This equation, along with the natural boundary and initial conditions, has only the trivial solution, i.e. explosion in finite time does not occur, provided the creation ra...

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Veröffentlicht in:Journal of applied probability 2016-09, Vol.53 (3), p.938-945
1. Verfasser: Erickson, K. Bruce
Format: Artikel
Sprache:eng
Schlagworte:
Boundaries
Diffusion
Explosions
Initial conditions
Markov processes
Mathematical analysis
Nonlinearity
Partial differential equations
Particle diffusion
Probability
Rectangles
Research Papers
Short Communications
Studies
Uniqueness
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Beschreibung
Zusammenfassung:The explosion probability before time t of a branching diffusion satisfies a nonlinear parabolic partial differential equation. This equation, along with the natural boundary and initial conditions, has only the trivial solution, i.e. explosion in finite time does not occur, provided the creation rate does not grow faster than the square power at ∞.
ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2016.52