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dc.contributor.advisorDshalalow, Jewgeni H.
dc.contributor.authorAl-Obaidi, Ali Hussein Mahmood 2019
dc.descriptionThesis (Ph.D.) - Florida Institute of Technology, 2019.en_US
dc.description.abstractOur work deals with classes of random measures on σ-compact Hausdorff spaces perturbed by stochastic processes. We render a rigorous construction of the stochastic integral of functions of two variables and show that such an integral is a random measure. We establish a new Campbell-type formula that, along with a rigorous construction of modulation, leads to the intensity of a modulated random measure. We further introduce and study a marked Poisson random measure on a σ- compact Hausdorff space. The underlying parameters of this measure are changing in accordance with the evolution of a stochastic process. This generalized random measure has properties resembling those of the conventional Poisson random measure. We obtain an explicit formula for the probability distribution of such measure in the form of the Fourier- Stieltjes functional, show other notable properties including continuity in probability and quasi-independent increments, and discuss various applications of the generalized Poisson measure (modulated by a semi- Markov process) to astrophysics and finance.en_US
dc.rightsCC BY 4.0en_US
dc.subjectPoisson random measureen_US
dc.subjectCox random measureen_US
dc.subjectStochastic intensitiesen_US
dc.subjectCampbell's formulaen_US
dc.subjectStochastic financeen_US
dc.subjectSemi-Markov modulated random measuresen_US
dc.subjectStochastic controlen_US
dc.titleGeneralized Random Measures on Topological Spacesen_US
dc.typeDissertationen_US of Philosophy in Applied Mathematicsen_US Mathematicsen_US Sciencesen_US Institute of Technologyen_US

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CC BY 4.0
Except where otherwise noted, this item's license is described as CC BY 4.0