Some stochastic integral and discrete equations of the volterra and fredholm types with applications

Simple item page
dc.contributor.authorPadgett, W. J.en
dc.contributor.committeechairTsokos, Chris P.en
dc.contributor.committeememberHarshbarger, Boyden
dc.contributor.committeememberHamdan, Mohammed A.en
dc.contributor.committeememberArnold, Jesse C.en
dc.contributor.committeememberPace, W. Emoryen
dc.contributor.departmentStatisticsen
dc.date.accessioned2014-03-14T21:11:43Zen
dc.date.adate2010-06-02en
dc.date.available2014-03-14T21:11:43Zen
dc.date.issued1971-01-04en
dc.date.rdate2010-06-02en
dc.date.sdate2010-06-02en
dc.description.abstractRandom or stochastic integral equations occur frequently in the mathematical description of random phenomena in engineering, physics, biology, and oceanography. The present study is concerned with random or stochastic integral equations of the Volterra type in the form x(t;w) = h(tiW) + fa k(t,T~w)f(T,x(Tjw»dT, t > 0, and of the Fredholm type in the form 00 x(tjw) = h(t:w) + fa ko(t,T;w)e(T,x(T;w»dT, t ~ 0, where w £ Q, the supporting set of a complete probability measure space (n,A,p). A random function x(t:w} is said to be a random solution of an equation such as those above if it satisfies the equation with probability one. It is also required that X(tiW) be a second order stochastic process. The purpose of this dissertation is to investigate the existence, uniqueness, and stochastic stability properties of a random solution of these Volterra and Fredholm stochastic integral equations using the "theory of admissibility" and probabilistic functional analysis. The techniques of successive approximations and stochastic approximation are employed to approximate the random solution of the stochastic Volterra integral equation, and the convergence of the approximations to the unique random solution in mean square and with probability one is proven. Problems in telephone traffic theory, hereditary mechanics, population growth, and stochastic control theory are formulated, and some of the results of the investigation are applied. Finally, a discrete version of the above random integral equations is given, and several theorems concerning the existence, uniqueness, and stochastic stability of a random solution of the discrete equation are proven. Approximation of the random solution of the discrete version is obtained, and its convergence to the random solution is studied. This work extends and generalizes the work done by C. P. Tsokos in Mathematical Systems Theory 3 {1969}, pages 222-231, and M. W. Anderson in his Ph.D. dissertation at the University of Tennessee, 1966, among others. Extensions:of this research to several areas of application are proposed.en
dc.description.degreePh. D.en
dc.format.extent172 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-06022010-020350en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06022010-020350/en
dc.identifier.urihttp://hdl.handle.net/10919/37934en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1971.P33.pdfen
dc.relation.isformatofOCLC# 09362816en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectstatisticsen
dc.subjectmathematical systems theoryen
dc.subject.lccLD5655.V856 1971.P33en
dc.titleSome stochastic integral and discrete equations of the volterra and fredholm types with applicationsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineStatisticsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
LD5655.V856_1971.P33.pdf
Size:
5.27 MB
Format:
Adobe Portable Document Format
Download

Collections

Doctoral Dissertations