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

Ryu, K.; Im, M.

doi:10.1090/S0002-9947-02-03077-5

A measure-valued analogue of Wiener measure and the measure-valued Feynman-Kac formula
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by K. S. Ryu and M. K. Im

Trans. Amer. Math. Soc. 354 (2002), 4921-4951

DOI: https://doi.org/10.1090/S0002-9947-02-03077-5

Published electronically: July 23, 2002

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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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