Two-parameter Stochastic Processes With Finite Variation
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Abstract: Let E be a Banach space with norm ¿ , and f: R2+ ?E a function with finite variation. Properties of the variation are studied, and an associated increasing real-valued function f is defined. Sufficient conditions are given for f to have properties analogous to those of functions of one variable. A correspondence f ??f between such functions and E-valued Borel measures on R2+ is established, and the equality ?f = ? f is proved. Correspondences between E-valued two-parameter processes X with finite variation x and E-valued stochastic measures with finite variation are establi...
Abstract: Let E be a Banach space with norm ¿ , and f: R2+ ?E a function with finite variation. Properties of the variation are studied, and an associated increasing real-valued function f is defined. Sufficient conditions are given for f to have properties analogous to those of functions of one variable. A correspondence f ??f between such functions and E-valued Borel measures on R2+ is established, and the equality ?f = ? f is proved. Correspondences between E-valued two-parameter processes X with finite variation x and E-valued stochastic measures with finite variation are established. The case where X takes values in L(E,F) (F a Banach space) is studied, and it is shown that the associated measure ?x takes values in L(E,F"); some x sufficient conditions for y to be L(E,F)-valued are given. Similar results for the converse problem are established, and some conditions sufficient for the equality ?x = ? x are given. Dissertation Discovery Company and University of Florida are dedicated to making scholarly works more discoverable and accessible throughout the world. This dissertation, "Two-parameter Stochastic Processes With Finite Variation" by Charles Lindsey, was obtained from University of Florida and is being sold with permission from the author. A digital copy of this work may also be found in the university's institutional repository, IR@UF. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation.
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