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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A measure-valued analogue of Wiener measure and the measure-valued Feynman-Kac formula


Authors: K. S. Ryu and M. K. Im
Journal: Trans. Amer. Math. Soc. 354 (2002), 4921-4951
MSC (2000): Primary 28C35, 28C20, 45D05, 47A56
Published electronically: July 23, 2002
MathSciNet review: 1926843
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Abstract: In this article, we consider a complex-valued and a measure-valued measure on $C [0,t]$, the space of all real-valued continuous functions on $[0,t]$. Using these concepts, we establish the measure-valued Feynman-Kac formula and we prove that this formula satisfies a Volterra integral equation. The work here is patterned to some extent on earlier works by Kluvanek in 1983 and by Lapidus in 1987, but the present setting requires a number of new concepts and results.


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Additional Information

K. S. Ryu
Affiliation: Department of Mathematics, Han Nam University, Taejon 306-791, Korea
Email: ksr@math.hannam.ac.kr

M. K. Im
Affiliation: Department of Mathematics, Han Nam University, Taejon 306-791, Korea
Email: mki@mail.hannam.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03077-5
PII: S 0002-9947(02)03077-5
Keywords: Analogue of Wiener measure, Bartle integral, measure-valued Feynman-Kac formula, Volterra integral equation
Received by editor(s): December 18, 2001
Received by editor(s) in revised form: April 1, 2002
Published electronically: July 23, 2002
Dedicated: Dedicated to Professor Kun Soo Chang on his sixtieth birthday
Article copyright: © Copyright 2002 American Mathematical Society