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  • Representations of fractional Brownian motion

    Creator:
    Wichitsongkram, Noppadon
    Abstract:
    Integral representations provide a useful framework of study and simulation of fractional Browian motion, which has been used in modeling of many natural situations. In this thesis we extend an integral representation of fractional Brownian motion that is supported on a bounded interval of ℝ to integral representation that is...
    Resource Type:
    Dissertation
    Full Text:
    Representations of Fractional Brownian Motion AN

  • Some results in probability from the functional analytic viewpoint

    Creator:
    Gelbaum, Zachary A.
    Abstract:
    This dissertation presents some results from various areas of probability theory, the unifying theme being the use of functional analytic intuition and techniques. We first give a result regarding the existence of certain stochastic integral representations for Banach space valued Gaussian random variables. Next we give a spectral geometric construction...
    Resource Type:
    Dissertation
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    consider in the following chapters. Brownian motion, Bt, t ∈ [0, 1], is the fundamental example of a

  • Skew Brownian motion and branching processes applied to diffusion-advection in heterogenous media and fluid flow

    Creator:
    Ramirez, Jorge M.
    Abstract:
    This thesis contains three manuscripts addressing the application of stochastic processes to the analysis and solution of partial differential equations (PDEs) in mathematical physics. In the first manuscript, one dimensional diffusion and Burgers equation are considered. The Fourier transform of the solution to each PDE is represented as the expected...
    Resource Type:
    Dissertation
    Full Text:
    Doctor of Philosophy in Mathematics presented on June 28, 2007. Title: Skew Brownian Motion and

  • Ruin Problems with Risky Investments

    Creator:
    Loke, Sooie-Hoe
    Abstract:
    In this dissertation, we study two risk models. First, we consider the dual risk process which models the surplus of a company that incurs expenses at a constant rate and earns random positive gains at random times. When the surplus is invested in a risky asset following a geometric Brownian...
    Resource Type:
    Dissertation
    Full Text:
    times. When the surplus is invested in a risky asset following a geometric Brownian motion, we show