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THE BARTLE INTEGRAL AND THE CONDITIONAL WIENER INTEGRAL ON C[0,t]
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 Title & Authors
THE BARTLE INTEGRAL AND THE CONDITIONAL WIENER INTEGRAL ON C[0,t]
Ryu, Kun-Sik; Im, Man-Kyu;
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 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;
 Language
English
 Cited by
 References
1.
K. S. Chang and J. S. Chang, Evaluation of some conditional Wiener integrals, Bull. Korean Math. Soc. 21 (1984), 99-106.

2.
J. Diestel and J. J. Uhl, Vector measures, Mathematical Survey, no. 15, Amer. Math. Soc., 1977.

3.
N. Dunford and J. T. Schwartz, Linear operators, part I, General theory, Pure and Applied Mathematics, Vol. VII, Wiley Interscience, New York, 1958.

4.
G. W. Johnson and M. L. Lapidus, The Feynman integral and Feynman's operational calculus, Oxford Math. Monogr., Oxford Univ. Press, 2000.

5.
D. R. Lewis, Integration with respect to vector measure, Pacific J. Math. 33 (1970), no. 1, 157-165. crossref(new window)

6.
C. Park and D. L. Skoug, A simple formula for conditional Wiener integrals with applications, Pacific. J. Math. 135 (1988), no. 2, 381-394. crossref(new window)

7.
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. crossref(new window)

8.
K. S. Ryu, An analogue of Wiener measure and its applications, J. Korean Math. Soc. 39 (2002), no. 5, 801-819. crossref(new window)

9.
H. G. Tucker, A graduate course in probability, Academic Press, 1967.

10.
J. Yeh, Inversion of conditional expectations, Pacific J. Math. 52 (1974), no. 2, 631-640. crossref(new window)

11.
J. Yeh, Inversion of conditional Wiener integrals, Pacific J. Math. 59 (1975), no. 2, 623-638. crossref(new window)

12.
J. Yeh, Stochastic processes and the Wiener integral, Marcel Deckker, New York, 1973.