Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.

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Description:: This thesis is a large deviations study for the performance of an interacting particle method for rare event estimation. The analysis is restricted to a …
Year:: 2012
Contributor:: Cai, Yi (creator); Dupuis, Paul (Director); Dong, Hongjie (Reader); Ramanan, Kavita (Reader); Brown University. Applied Mathematics (sponsor)
Genre:: theses
Subject:: interacting particle system; weak convergence approach; Large deviations
Language:: English
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: This thesis studies the application of the Wiener chaos expansion in the analysis of stochastic partial differential equations (SPDEs). Specifically, linear parabolic SPDEs and the …
Year:: 2011
Contributor:: Lee, Chia Ying (creator); Rozovsky, Boris (Director); Karniadakis, George (Reader); Ramanan, Kavita (Reader); Brown University. Applied Mathematics (sponsor)
Genre:: theses
Subject:: Wiener chaos expansion; stochastic finite element method; stochastic Navier-Stokes equation; Stochastic partial differential equations; Malliavin calculus
Language:: English
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: The subject of this thesis is the development of a stochastic process that can be interpreted as a model of grain coarsening, a central problem …
Year:: 2014
Contributor:: Klobusicky, Joe J (creator); Menon, Govind (Director); Ramanan, Kavita (Reader); Pego, Robert (Reader); Brown University. Applied Mathematics (sponsor)
Genre:: theses
Subject:: grain coarsening; kinetic equations; Markov processes
Language:: English
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: This thesis considers a feed-forward network with a single server station serving jobs with multiple levels of priority. The service discipline is preemptive in that …
Year:: 2012
Contributor:: Setayeshgar, Leila (creator); Wang, Hui (Director); Blanchet, Jose (Reader); Holmer, Justin (Reader); Ramanan, Kavita (Reader); Brown University. Applied Mathematics (sponsor)
Genre:: theses
Subject:: Weak Convergence; Discontinuous Dynamics; Large deviations
Language:: English
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: In this thesis, we use the large deviations principle to characterize the rate of convergence of the empirical measures of Markov processes. An explicit formula …
Year:: 2013
Contributor:: Liu, Yufei (creator); Dupuis, Paul (Director); Doll, Jimmie (Reader); Ramanan, Kavita (Reader); Brown University. Applied Mathematics (sponsor)
Genre:: theses
Subject:: empirical measure; Markov jump process; Markov chain Monte Carlo; Large deviations
Language:: English
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: We prove a moderate deviations principle for the continuous time linear interpolation of discrete time recursive stochastic processes, and then investigate importance sampling schemes based …
Year:: 2015
Contributor:: Johnson, Dane Michael (creator); Dupuis, Paul (Director); Ramanan, Kavita (Reader); Budhiraja, Amarjit (Reader); Brown University. Applied Mathematics (sponsor)
Genre:: theses
Subject:: Weak Convergence; Importance Sampling; Large deviations
Language:: English
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: This thesis studies the integral of an exponential function over an adjoint orbit of a compact Lie group. These integrals are named after Harish-Chandra, who …
Year:: 2020
Contributor:: McSwiggen, Colin Smith (creator); Menon, Govind (Advisor); Zuber, Jean-Bernard (Reader); Novak, Jonathan (Reader); Ramanan, Kavita (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Combinatorics; Applied mathematics; Mathematical physics; Representations of Lie algebras; Random matrices; Functions, Special
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: Modern probabilistic models involve computation and analysis in very high-dimensional spaces. Here we explore several of ways in which analysis of problems high dimensional spaces …
Year:: 2017
Contributor:: Loper, Jackson Hoy (creator); Geman, Stuart (Advisor); Ramanan, Kavita (Reader); Harrison, Matthew (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Machine Learning; Poisson processes; Biometry; Brownian motion processes
Collection:: Applied Mathematics; Theses and Dissertations

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