Uniqueness of the null solution to a nonlinear partial differential equation satisfied by the explosion probability of a branching diffusion.(English)Zbl 1351.60112

Summary: 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 $$\infty$$.

MSC:

 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness 35K59 Quasilinear parabolic equations 60K99 Special processes
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