Browsing by Author "Koralov, L"

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    Asymptotic behavior of branching diffusion processes in periodic media
    Hebbar, P; Koralov, L; Nolen, J
    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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    Multi-type branching processes with time-dependent branching rates
    (Journal of Applied Probability, 2018-09-01) Dolgopyat, D; Hebbar, P; Koralov, L; Perlman, M
    Copyright © Applied Probability Trust 2018. Under mild nondegeneracy assumptions on branching rates in each generation, we provide a criterion for almost sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total number of particles (conditioned on survival and divided by the expectation of the resulting random variable) to approach an exponential random variable as time goes to ∞.