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Conditional transform with respect to the Gaussian process involving the conditional convolution product and the first variation

이일용|장승준|정현수
대한수학회 (The Korean Mathematical Society)|2014.11|대한수학회보 (Bulletin of the KMS)|제51권 제6호|pp. 1561-1577

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참고문헌

키워드

Gaussian processconditional convolution productBrownian motion processWiener integralsimple formula
주제분류수학

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 Sα [5, 8].

Abstract

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 Sα [5, 8].

참고문헌 (16)

  1. R. H. Cameron, "Some examples of Fourier-Wiener transforms of analytic functionals", Duke Math. J, 12, pp.485~488 (1945)
  2. R. H. Cameron, "Fourier-Wiener transforms of functionals belonging to L2 over the space C", Duke Math. J, 14, pp.99~107 (1947)
  3. S. J. Chang, "Some basic relationships among transforms, convolution products, first variations and inverse transforms", Cent. Eur. J. Math, 11(3), pp.538~551 (2013)
  4. J. G. Choi, "A rotation on Wiener space with applications", ISRN Appl. Math, 2012, pp.13~ (2012)
  5. H. S. Chung, "Conditional integral transforms with related topics on function space", Filomat, 26(6), pp.1151~1162 (2012)
  6. D. M. Chung, "Generalized Feynman integrals via conditional Feynman integrals", Michigan Math. J, 40(2), pp.337~391 (1993)
  7. H. S. Chung, "Relationships involving transform and convo-lutions via the translation theorem", Stoch. Anal. Appl, 32(2), pp.348~363 (2014)
  8. H. S. Chung, "Generalized integral transforms and convolution products on function space", Integral Transforms Spec. Funct, 22(8), pp.573~586 (2011)
  9. D. L. Cohn, "Measure Theory" (1980), Birkh¨auser-Verlag
  10. G. W. Johnson, "Scale-invariant measurability in Wiener space", Pacific J. Math, 83(1), pp.157~176 (1979)
  11. B. J. Kim, "Conditional integral transforms, conditional convolution products and first variations for some conditioning functions", Far East J. Math. Sci, 19(3), pp.245~258 (2005)
  12. B. S. Kim, "Conditional integral transforms, conditional con-volution products and first variations", Panamer. Amer. Math. J, 14(3), pp.27~47 (2004)
  13. ), "Rocky Mountain J. Math", 2003, 1379~1393
  14. I. Y. Lee, "Relationships among the transform with respect to the Gaussian process, the product and the first variation of functionals on function space", ~
  15. C. Park, "A simple formula for conditional Wiener integrals with applica-tions", Pacific J. Math, 135(2), pp.381~394 (1988)
  16. W. Rudin, "Real and Complex Analysis" (1966), McGraw-Hill

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