Two-parameter Stochastic Processes With Finite Variation - Hardcover

Lindsey, Charles

Hardcover

ISBN 10: 0530005158 ISBN 13: 9780530005157

Publisher: Dissertation Discovery Company, 2019

Synopsis

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.

Edition details

• Publisher: Dissertation Discovery Company
• Publication date: 2019
• Language: English
• ISBN 10: 0530005158
• ISBN 13: 9780530005157
• Binding: Hardcover
• Number of pages: 160