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September 2016 Uniqueness of the null solution to a nonlinear partial differential equation satisfied by the explosion probability of a branching diffusion
K. Bruce Erickson
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J. Appl. Probab. 53(3): 938-945 (September 2016).

Abstract

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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K. Bruce Erickson. "Uniqueness of the null solution to a nonlinear partial differential equation satisfied by the explosion probability of a branching diffusion." J. Appl. Probab. 53 (3) 938 - 945, September 2016.

Information

Published: September 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1351.60112
MathSciNet: MR3570106

Subjects:
Primary: 35A02 , 35K59 , 60J80 , 60K99

Keywords: Bessel , branching diffusion , probability of explosion , Quasi-linear

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 3 • September 2016
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