대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제51권6호
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  • Pages.1561-1577
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  • 2014
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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CONDITIONAL TRANSFORM WITH RESPECT TO THE GAUSSIAN PROCESS INVOLVING THE CONDITIONAL CONVOLUTION PRODUCT AND THE FIRST VARIATION

  • 투고 : 2013.04.16
  • 발행 : 2014.11.30
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초록

In this paper, we define a conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation of functionals via the Gaussian process. We then examine various relationships of the conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation for functionals F in $S_{\alpha}$ [5, 8].

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과제정보

연구 과제 주관 기관 : Dankook University

참고문헌

  1. R. H. Cameron, Some examples of Fourier-Wiener transforms of analytic functionals, Duke Math. J. 12 (1945), 485-488. https://doi.org/10.1215/S0012-7094-45-01243-9
  2. R. H. Cameron and W. T. Martin, Fourier-Wiener transforms of functionals belonging to $L_2$ over the space C, Duke Math. J. 14 (1947), 99-107. https://doi.org/10.1215/S0012-7094-47-01409-9
  3. S. J. Chang, H. S. Chung, and D. Skoug, Some basic relationships among transforms, convolution products, first variations and inverse transforms, Cent. Eur. J. Math. 11 (2013), no. 3, 538-551. https://doi.org/10.2478/s11533-012-0148-x
  4. J. G. Choi and S. J. Chang, A rotation on Wiener space with applications, ISRN Appl. Math. 2012 (2012), Art. ID 578174, 13 pages.
  5. H. S. Chung, J. G. Choi, and S. J. Chang, Conditional integral transforms with related topics on function space, Filomat 26 (2012), no. 6, 1151-1162. https://doi.org/10.2298/FIL1206151C
  6. D. M. Chung, C. Park, and D. Skoug, Generalized Feynman integrals via conditional Feynman integrals, Michigan Math. J. 40 (1993), no. 2, 337-391. https://doi.org/10.1307/mmj/1029004758
  7. H. S. Chung, D. Skoug, and S. J. Chang, Relationships involving transform and convolutions via the translation theorem, Stoch. Anal. Appl. 32 (2014), no. 2, 348-363. https://doi.org/10.1080/07362994.2013.877350
  8. H. S. Chung and V. K. Tuan, Generalized integral transforms and convolution products on function space, Integral Transforms Spec. Funct. 22 (2011), no. 8, 573-586. https://doi.org/10.1080/10652469.2010.535798
  9. D. L. Cohn, Measure Theory, Birkhauser-Verlag, Boston, 1980.
  10. G. W. Johnson and D. L. Skoug, Scale-invariant measurability in Wiener space, Pacific J. Math. 83 (1979), no. 1, 157-176. https://doi.org/10.2140/pjm.1979.83.157
  11. B. J. Kim, Conditional integral transforms, conditional convolution products and first variations for some conditioning functions, Far East J. Math. Sci. 19 (2005), no. 3, 245-258.
  12. B. S. Kim, B. J. Kim, and D. Skoug, Conditional integral transforms, conditional convolution products and first variations, Panamer. Amer. Math. J. 14 (2004), no. 3, 27-47.
  13. B. S. Kim and D. Skoug, Integral transforms of functionals in $L_2(C_0$[0, T]), Rocky Mountain J. Math. 33 (2003), no. 4, 1379-1393. https://doi.org/10.1216/rmjm/1181075469
  14. I. Y. Lee, H. S. Chung, and S. J. Chang, Relationships among the transform with respect to the Gaussian process, the ${\diamond}$-product and the first variation of functionals on function space, to submitted for publications.
  15. C. Park and D. Skoug, A simple formula for conditional Wiener integrals with applications, Pacific J. Math. 135 (1988), no. 2, 381-394. https://doi.org/10.2140/pjm.1988.135.381
  16. W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966.

피인용 문헌

  1. Series expansions of the transform with respect to the Gaussian process vol.26, pp.4, 2015, https://doi.org/10.1080/10652469.2014.991920
  2. Generalized conditional transform with respect to the Gaussian process on function space vol.26, pp.12, 2015, https://doi.org/10.1080/10652469.2015.1070149