Two-parameter Stochastic Processes With Finite Variation

By Charles Lindsey

Book Overview

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.

• Format: Paperback
• Language: English
• ISBN: 053000514X
• ISBN13: 9780530005140
• Release Date: May 2019
• Publisher: Dissertation Discovery Company
• Length: 160 Pages
• Weight: 0.85 lbs.
• Dimensions: 0.3" x 8.5" x 11.0"