[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2010.23.4.711

AN INTEGRATION FORMULA FOR ANALOGUE OF WIENER MEASURE AND ITS APPLICATIONS

Ryu, Kun Sik (Department of Mathematics Educations Hannam University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.23, no.4, 2010 , pp. 711-720 More about this Journal

Abstract

In this note, we will establish the integration formulae for functionals such as $F(x)=\prod_{j=1}^{n}\;x(s_j)^2$ and $G(x)=\exp\{{\lambda}{\int}_{0}^{t}\;x(s)^2dm_L(s)\}$ in the analogue of Wiener measure space and using our formulae, we will derive some formulae for series.

Keywords

Wiener measure space; analogue of Wiener measure space; Dirichilet's integral; the generalized Fernique theorem; translation theorem;

Citations & Related Records

Times Cited By KSCI : 5 (Citation Analysis)

Reference
Cited By KSCI

1	T. S. Chiang, Y. Chow and Y. J. Lee, A formula for EW exp $-2^{-1}a^{2}II{x+y}II^{2}_{2}$ }, Proc. Amer. Math. Soc. 100 (1987), 721-724.
2	C. George, Exercises in integration, Springer-Verlag New York, 1984.
3	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), 4921-4951. DOI ScienceOn
4	K. S. Ryu and M. K. Im, An analogue of Wiener measure and its applications, J. Korean Math. Soc. 39 (2002), 801-819. 과학기술학회마을 DOI ScienceOn
5	K. S. Ryu, The operational calculus for a measure-valued Dyson series, J. Korean Math. Soc. 43 (2006), 703-715. 과학기술학회마을 DOI
6	K. S. Ryu, The Dobrakov integral over paths, J. Chungcheong Math. Soc. 19 (2006), 61-68.
7	K. S. Ryu and M. K. Im, The measure-valued Dyson series and its stability theorem, J. Korean Math. Soc. 43 (2006), 461-489. 과학기술학회마을 DOI
8	K. S. Ryu, The simple formula of conditional expectation on analogue of Wiener measure, Honam Math. J. 30 (2008), 723-732. DOI ScienceOn
9	K. S. Ryu and S. H. Shim, The rotation theorem on analogue of Wiener mea- sure, Honam Math. J. 29 (2007), 577-588. DOI ScienceOn
10	K. S. Ryu, The generalized Fernique's theorem for analogue of Wiener measure space, J. Chungcheong Math. Soc. 22 (2009), 743-748.
11	N. Wiener, Differential space, J. Math. Phys. 2 (1923), 131-174. DOI