Theses and Dissertations from UMD

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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM

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Author: search.filters.author.Hebbar, PratimaSubject: search.filters.subject.Dynamical systems

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    Branching diffusion processes in periodic media
    (2019) Hebbar, Pratima; Koralov, Leonid; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    In the first part of this manuscript, we investigate the asymptotic behavior of solutions to parabolic partial differential equations (PDEs) in $\real^d$ with space-periodic diffusion matrix, drift, and potential. The asymptotics is obtained up to linear in time distances from the support of the initial function. Using this asymptotics, we describe the 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. In the second part of the manuscript, we obtain asymptotic expansions for the distribution functions of continuous time stochastic processes with weakly dependent increments in the domain of large deviations. As a key example, we show that additive functionals of solutions of stochastic differential equations (SDEs) satisfying H\"ormander condition on a $d$--dimensional compact manifold admit asymptotic expansions of all orders in the domain of large deviations.