Open Access
2020 Asymptotic behavior of branching diffusion processes in periodic media
Pratima Hebbar, Leonid Koralov, James Nolen
Electron. J. Probab. 25: 1-40 (2020). DOI: 10.1214/20-EJP527


We study the asymptotic behavior of branching diffusion processes in periodic media. For a super-critical branching process, we distinguish two types of behavior for the normalized number of particles in a bounded domain, depending on the distance of the domain from the region where the bulk of the particles is located. At distances that grow linearly in time, we observe intermittency (i.e., the $k$-th moment dominates the $k$-th power of the first moment for some $k$), while, at distances that grow sub-linearly in time, we show that all the moments converge. A key ingredient in our analysis is a sharp estimate of the transition kernel for the branching process, valid up to linear in time distances from the location of the initial particle.


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Pratima Hebbar. Leonid Koralov. James Nolen. "Asymptotic behavior of branching diffusion processes in periodic media." Electron. J. Probab. 25 1 - 40, 2020.


Received: 4 March 2020; Accepted: 28 September 2020; Published: 2020
First available in Project Euclid: 15 October 2020

MathSciNet: MR4162842
Digital Object Identifier: 10.1214/20-EJP527

Primary: 35K10 , 60J60 , 60J80

Keywords: Branching diffusions , Intermittency , large deviations , parabolic PDEs

Vol.25 • 2020
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