Asymptotic behavior of branching diffusion processes in periodic media
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Abstract
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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https://hdl.handle.net/10161/20254Collections
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Pratima Hebbar
Phillip Griffiths Assistant Research Professor
I am a Griffiths Assistant Research Professor at the Department of Mathematics at
Duke University. Prior to arriving at Duke, I completed my Ph.D. from the Department
of Mathematics at the University of Maryland. The main focus of my research is asymptotic
problems arising from Branching Processes, Branching Diffusions and related Dynamical
Systems.
James H. Nolen
Professor of Mathematics
I study partial differential equations and probability, which have been used to model
many phenomena in the natural sciences and engineering. In some cases, the parameters
for a partial differential equation are known only approximately, or they may have
fluctuations that are best described statistically. So, I am especially interested
in differential equations modeling random phenomena and whether one can describe the
statistical properties of solutions to these equations. Asymptotic anal
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