Branching diffusion processes in periodic media

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dc.contributor.advisorKoralov, Leoniden_US
dc.contributor.authorHebbar, Pratimaen_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2019-09-26T05:34:59Z
dc.date.available2019-09-26T05:34:59Z
dc.date.issued2019en_US
dc.description.abstractIn 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.en_US
dc.identifierhttps://doi.org/10.13016/6w8x-dvow
dc.identifier.urihttp://hdl.handle.net/1903/24955
dc.language.isoenen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledStatisticsen_US
dc.subject.pquncontrolledBranching processesen_US
dc.subject.pquncontrolledDiffusion processesen_US
dc.subject.pquncontrolledDynamical systemsen_US
dc.subject.pquncontrolledProbabilityen_US
dc.subject.pquncontrolledStochastic processesen_US
dc.titleBranching diffusion processes in periodic mediaen_US
dc.typeDissertationen_US

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