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Generalized Random Measures On Topological Spaces, Ali Hussein Mahmood Al-Obaidi

Theses and Dissertations

Our work deals with classes of random measures on -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 - compact Hausdorff space. The underlying parameters of this measure are changing in accordance with the evolution of a stochastic process. This generalized random measure …