Acknowledgement
Supported by : Kyonggi University
This work was supported by Kyonggi University Research Grant 2018.
References
- R. H. Cameron and W. T. Martin, Transformations of Wiener integrals under translations, Ann. of Math. (2) 45 (1944), 386-396. https://doi.org/10.2307/1969276
- D. H. Cho, A simple formula for an analogue of conditional Wiener integrals and its applications, Trans. Amer. Math. Soc. 360 (2008), no. 7, 3795-3811. https://doi.org/10.1090/S0002-9947-08-04380-8
- D. H. Cho, A simple formula for an analogue of conditional Wiener integrals and its applications. II, Czechoslovak Math. J. 59(134) (2009), no. 2, 431-452. https://doi.org/10.1007/s10587-009-0030-6
- D. H. Cho, Measurable functions similar to the Ito integral and the Paley-Wiener-Zygmund integral over continuous paths, Filomat 32 (2018), no. 18, 6441-6456. https://doi.org/10.2298/fil1818441c
- D. H. Cho, An evaluation formula for Radon-Nikodym derivatives similar to conditional expectations over paths, Mathematica Slovaca (2019), submitted.
- M. K. Im and K. S. Ryu, An analogue of Wiener measure and its applications, J. Korean Math. Soc. 39 (2002), no. 5, 801-819. https://doi.org/10.4134/JKMS.2002.39.5.801
- C. Park and D. Skoug, A simple formula for conditional Wiener integrals with applications, Pacific J. Math. 135 (1988), no. 2, 381-394. http://projecteuclid.org/euclid.pjm/1102688300 https://doi.org/10.2140/pjm.1988.135.381
- K. S. Ryu, The simple formula of conditional expectation on analogue of Wiener measure, Honam Math. J. 30 (2008), no. 4, 723-732. https://doi.org/10.5831/HMJ.2008.30.4.723
- K. S. Ryu, The generalized analogue of Wiener measure space and its properties, Honam Math. J. 32 (2010), no. 4, 633-642. https://doi.org/10.5831/HMJ.2010.32.4.633
- K. S. Ryu, The translation theorem on the generalized analogue of Wiener space and its applications, J. Chungcheong Math. Soc. 26 (2013), no. 4, 735-742. https://doi.org/10.14403/jcms.2013.26.4.735
- J. Yeh, Transformation of conditional Wiener integrals under translation and the Cameron-Martin translation theorem, Tohoku Math. J. (2) 30 (1978), no. 4, 505-515. https://doi.org/10.2748/tmj/1178229910