Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Pa-tial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
TWO-PARAMETER STOCHASTIC PROCESSES
WITH FINITE VARIATION
BY
CHARLES LINDSEY
April, 1988
Chair: Nicolae Dinculeanu
Major Department: Mathematics
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Let E be a Banach space with norm I1||, and f: R + E a function
with finite variation. Properties of the variation are studied, and
an associated increasing real-valued function IfJ is defined.
Sufficient conditions are given for f to have properties analogous to
those of functions of one variable. A correspondence f + pf between
such functions and E-valued Borel measures on R is established, and
the equality |uf| = ifl is proved. Correspondences between E-valued
two-parameter processes X with finite variation IXI 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 p takes values in L(E,F"); some
sufficient conditions for px to be L(E,F)-valued are given. Similar
results for the converse problem are established, and some conditions
sufficient for the equality \ux = pUXI are given.
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