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Change of scale formulas for conditional Wiener integrals as integral transforms over Wiener paths in abstract Wiener space

조동현
대한수학회 (The Korean Mathematical Society)|2007.01|대한수학회논문집 (Communications of the KMS)|제22권 제1호|pp. 91-109

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Abstract

iener integrals, as integral transforms, of possibly unbounded functions over Wiener paths in abstract Wiener space. In fact, we derive the change of scale formula for the product of the functions in a Banach algebra which is equivalent to both the Fresnel class and the space of mea- sures of bounded variation over a real separable Hilbert space, and the Lp-type cylinder functions over Wiener paths in abstract Wiener space. As an application of the result, we obtain a change of scale formula for the conditional analytic Fourier-Feynman transform of the product of the functions.

참고문헌 (15)

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  2. "The behavior of measure and measurability underchange of scale in Wiener space CHANGE OF SCALE FORMULAS FOR CONDITIONAL WIENER INTEGRALS 109" (1947)
  3. "Relationships between the Wiener integral andthe analytic Feynman integral" (1987)
  4. "Change of scale formulas for Wiener integral" (1987)
  5. "A conditional analytic Feynman integral overWiener paths in abstract Wiener space", 2(9), pp.855~870 (2002)
  6. "Functions in the Fresnel class" (1987)
  7. "A change of scale formula for Wienerintegrals of unbounded functions", 34(1), pp.371~389 (2004)
  8. "Conditional analytic Feynman integral over product space of Wiener pathsin abstract Wiener space to appear in Rocky Mount"
  9. "Generalized Feynman integrals using analytic continua-tion in several complex variables" (1984)
  10. "The law of the iterated logarithm for Brownian motion in aBanach space" (1973)
  11. "Gaussian measures in Banach spaces Lecture Notes in Mathematics 463" (1975), Springer-Verlag
  12. "The Wiener integral over paths in abstract Wiener space" (1992)
  13. "A change of scale formula for Wiener integrals on abstractWiener spaces" (1994)
  14. "A change of scale formula for Wiener integrals on abstract Wiener spaces II" (1994)
  15. "Change of scale formulas for Yeh-Wiener integrals" (1991)

관련 논문AI추천

A Change of scale formula for conditional Wiener integrals on classical Wiener space유일, 김병수, 송택섭, 장건수, 조동현대한수학회 · 대한수학회지2007 · 제44권 제4호Change of scale formulas for Wiener integral over paths in abstract Wiener space김병수, 김태수대한수학회 · 대한수학회논문집2006 · 제21권 제1호A change of scale formula for Wiener integrals of unbounded functions II유일, 김병수, 송특섭대한수학회 · 대한수학회논문집2006 · 제21권 제1호Conditional Fourier-Feynman transforms of variations over Wiener paths in abstract Wiener space조동현대한수학회 · 대한수학회지2006 · 제43권 제5호Conditional first variation over Wiener paths in abstract Wiener space조동현대한수학회 · 대한수학회지2005 · 제42권 제5호Scale transformations for present position-independent conditional expectationsDong Hyun Cho대한수학회 · 대한수학회지2016 · 제53권 제3호

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