Group Title: Vector measures and stochastic integration, by Franklin P. Witte
Title: Vector measures and stochastic integration
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Permanent Link: http://ufdc.ufl.edu/UF00097651/00001
 Material Information
Title: Vector measures and stochastic integration
Physical Description: v, 108 leaves. : 28 cm.
Language: English
Creator: Witte, Franklin Pierce, 1942- ( Dissertant )
Brooks, James K. ( Thesis advisor )
Varma, Arun K. ( Reviewer )
Dufty, James W. ( Reviewer )
Bedmarck, A. R. ( Degree grantor )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 1972
Copyright Date: 1972
 Subjects
Subjects / Keywords: Stochastic integrals   ( lcsh )
Measure theory   ( lcsh )
Mathematics thesis Ph. D
Dissertations, Academic -- Mathematics -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Abstract: This dissertation investigates the stochastic integration of scalar-valued functions from the point of view of vector measure and integration theory. We make a detailed study of abstract integration theory in Chapters I and II, and then apply our results in Chapter III to show that certain kinds of stochastic integrals, previously defined by other means, are special cases of the general theory. In carrying out this program we prove extended forms of the classical convergence theorems for integrals. We also establish a generalization of the standard extension theorem for scalar measures generated by a left continuous function of bounded variation. The special case of measures in Hilbert space is discussed, and a corrected form of a theorem of Cramer is proved. In Chapter III we show that certain sample path integrals, the Wiener-Doob integral, and a general martingale integral are included in the abstract integration theory. We establish a general existence theorem for stochastic integrals with respect to a martingale in L , 1 < p < infinity>.
Thesis: Thesis -- University of Florida.
Bibliography: Bibliography: leaves 105-107.
Original Version: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00097651
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000577567
oclc - 13989845
notis - ADA5262

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