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http://dx.doi.org/10.4134/CKMS.2004.19.4.643

THE BARTLE INTEGRAL AND THE CONDITIONAL WIENER INTEGRAL ON C[0,t]  

Ryu, Kun-Sik (Department of Mathematics Han Nam University)
Im, Man-Kyu (Department of Mathematics Han Nam University)
Publication Information
Communications of the Korean Mathematical Society / v.19, no.4, 2004 , pp. 643-660 More about this Journal
Abstract
In this paper, we give a new formula between the conditional Wiener integral E(F｜X), the conditional Wiener integral of F given X, and the integral with respect to a measure-valued measure, a kind of Bartle integral. Using this formula, we give some examples of evaluation of E(F｜X).
Keywords
Bartle integral; the conditional Wiener integral;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 J. Yeh, Inversion of conditional Wiener integrals, Pacific J. Math. 59 (1975), no. 2, 623-638.   DOI
2 J. Yeh, Stochastic processes and the Wiener integral, Marcel Deckker, New York, 1973.
3 K. S. Chang and J. S. Chang, Evaluation of some conditional Wiener integrals, Bull. Korean Math. Soc. 21 (1984), 99-106.   과학기술학회마을
4 J. Diestel and J. J. Uhl, Vector measures, Mathematical Survey, no. 15, Amer. Math. Soc., 1977.
5 N. Dunford and J. T. Schwartz, Linear operators, part I, General theory, Pure and Applied Mathematics, Vol. VII, Wiley Interscience, New York, 1958.
6 G. W. Johnson and M. L. Lapidus, The Feynman integral and Feynman's operational calculus, Oxford Math. Monogr., Oxford Univ. Press, 2000.
7 D. R. Lewis, Integration with respect to vector measure, Pacific J. Math. 33 (1970), no. 1, 157-165.   DOI
8 C. Park and D. L. Skoug, A simple formula for conditional Wiener integrals with applications, Pacific. J. Math. 135 (1988), no. 2, 381-394.   DOI
9 K. S. Ryu and M. K. Im, A measure-valued analogue of Wiener measure and the measure-valued Feynman-Kac formula, Trans. Amer. Math. Soc. 354 (2002), no. 12, 4921-4951.   DOI   ScienceOn
10 K. S. Ryu, An analogue of Wiener measure and its applications, J. Korean Math. Soc. 39 (2002), no. 5, 801-819.   과학기술학회마을   DOI   ScienceOn
11 H. G. Tucker, A graduate course in probability, Academic Press, 1967.
12 J. Yeh, Inversion of conditional expectations, Pacific J. Math. 52 (1974), no. 2, 631-640.   DOI