Document Zbl 1351.60112

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

J. Appl. Probab. 53, No. 3, 938-945 (2016).

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 \(\infty\).

Cited in 2 Documents

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

Keywords:

quasi-linear; branching diffusion; Bessel; probability of explosion

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