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Uniqueness of the null solution to a nonlinear partial differential equation satisfied by the explosion probability of a branching diffusion
Part of
K. Bruce Erickson
Journal:

Journal of Applied Probability / Volume 53 / Issue 3 / September 2016

Published online by Cambridge University Press:

24 October 2016, pp. 938-945

Print publication:

September 2016
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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 ∞.

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