본문 바로가기
HOME> 논문 > 논문 검색상세

논문 상세정보

Journal of the Korean Mathematical Society = 대한수학회지 v.44 no.4, 2007년, pp.1025 - 1050   피인용횟수: 4

A CHANGE OF SCALE FORMULA FOR CONDITIONAL WIENER INTEGRALS ON CLASSICAL WIENER SPACE

Yoo, Il   (DEPARTMENT OF MATHEMATICS YONSEI UNIVERSITYUU0000936  ); Chang, Kun-Soo   (DEPARTMENT OF MATHEMATICS YONSEI UNIVERSITYUU0000936  ); Cho, Dong-Hyun   (DEPARTMENT OF MATHEMATICS KYONGGI UNIVERSITYUU0000066  ); Kim, Byoung-Soo   (SCHOOL OS LIBERAL ARTS SEOUL NATIONAL UNIVERSITY OF TECHNOLOGYUU0000691  ); Song, Teuk-Seob   (DEPARTMENT OF COMPUTER ENGINEERING MOKWON UNIVERSITYUU0000545  );
  • 초록

    Let $X_k(x)=({\int}^T_o{\alpha}_1(s)dx(s),...,{\int}^T_o{\alpha}_k(s)dx(s))\;and\;X_{\tau}(x)=(x(t_1),...,x(t_k))$ on the classical Wiener space, where ${{\alpha}_1,...,{\alpha}_k}$ is an orthonormal subset of $L_2$ [0, T] and ${\tau}:0 is a partition of [0, T]. In this paper, we establish a change of scale formula for conditional Wiener integrals $E[G_{\gamma}|X_k]$ of functions on classical Wiener space having the form $$G_{\gamma}(x)=F(x){\Psi}({\int}^T_ov_1(s)dx(s),...,{\int}^T_o\;v_{\gamma}(s)dx(s))$$ , for $F{\in}S\;and\;{\Psi}={\psi}+{\phi}({\psi}{\in}L_p(\mathbb{R}^{\gamma}),\;{\phi}{\in}\hat{M}(\mathbb{R}^{\gamma}))$ , which need not be bounded or continuous. Here S is a Banach algebra on classical Wiener space and $\hat{M}(\mathbb{R}^{\gamma})$ is the space of Fourier transforms of measures of bounded variation over $\mathbb{R}^{\gamma}$ . As results of the formula, we derive a change of scale formula for the conditional Wiener integrals $E[G_{\gamma}|X_{\tau}]\;and\;E[F|X_{\tau}]$ . Finally, we show that the analytic Feynman integral of F can be expressed as a limit of a change of scale transformation of the conditional Wiener integral of F using an inversion formula which changes the conditional Wiener integral of F to an ordinary Wiener integral of F, and then we obtain another type of change of scale formula for Wiener integrals of F.


  • 주제어

    change of scale formula .   conditional analytic Feynman integral .   conditional analytic Wiener integral .   conditional Wiener integral.  

  • 참고문헌 (13)

    1. R. H. Cameron, The translation pathology of Wiener space, Duke Math. J. 21 (1954), 623-627 
    2. R. H. Cameron and W. T. Martin, The behavior of measure and measurability under change of scale in Wiener space, Bull. Amer. Math. Soc. 53 (1947), 130-137 
    3. R. H. Cameron and D. A. Storvick, Some Banach algebras of analytic Feynman integrable functionals, Lecture Notes in Math. 798, Springer-Verlag, New York (1980), 18-67 
    4. R. H. Cameron and D. A. Storvick, Relationships between the Wiener integral and the analytic Feynman integral, Rend. Circ. Mat. Palermo (2) Suppl. 17 (1987), 117-133 
    5. R. H. Cameron and D. A. Storvick, Change of scale formulas for Wiener integral, Rend. Circ. Mat. Palermo (2) Suppl. 17 (1987), 105-115 
    6. K. S. Chang, G. W. Johnson, and D. L. Skoug, Functions in the Fresnel class, Proc. Amer. Math. Soc. 100 (1987), no. 2, 309-318 
    7. D. M. Chung and D. L. Skoug, Conditional analytic Feynman integrals and a related Schrodinger integral equation, SIAM J. Math. Anal. 20 (1989), no. 4, 950-965 
    8. C. Park and D. L. Skoug, Conditional Wiener integrals II, Pacific J. Math. 167 (1995), no. 2, 293-312 
    9. C. Park and D. L. Skoug, A simple formula for conditional Wiener integrals with applications, Pacific J. Math. 135 (1988), no. 2, 381-394 
    10. I. Yoo and D. L. Skoug, A change of scale formula for Wiener integrals on abstract Wiener spaces, Internat. J. Math. Math. Sci. 17 (1994), no. 2, 239-247 
    11. I. Yoo, T. S. Song, B. S. Kim, and K. S. Chang, A change of scale formula for Wiener integrals of unbounded functions, Rocky Mountain J. Math. 34 (2004), no. 1, 371-389 
    12. I. Yoo and G. J. Yoon, Change of scale formulas for Yeh-Wiener integrals, Commun. Korean Math. Soc. 6 (1991), no. 1, 19-26 
    13. I. Yoo and D. L. Skoug, A change of scale formula for Wiener integrals on abstract Wiener spaces II, J. Korean Math. Soc. 31 (1994), no. 1, 115-129 
  • 이 논문을 인용한 문헌 (4)

    1. 2011. "" 충청수학회지 = Journal of the Chungcheong Mathematical Society, 24(3): 517~528     
    2. 2013. "" 충청수학회지 = Journal of the Chungcheong Mathematical Society, 26(1): 111~123     
    3. 2016. "" Journal of the Korean Mathematical Society = 대한수학회지, 53(3): 709~723     
    4. 2016. "" Bulletin of the Korean Mathematical Society = 대한수학회보, 53(5): 1531~1548     

 활용도 분석

  • 상세보기

    amChart 영역
  • 원문보기

    amChart 영역

원문보기

무료다운로드
유료다운로드
  • 원문이 없습니다.

유료 다운로드의 경우 해당 사이트의 정책에 따라 신규 회원가입, 로그인, 유료 구매 등이 필요할 수 있습니다. 해당 사이트에서 발생하는 귀하의 모든 정보활동은 NDSL의 서비스 정책과 무관합니다.

원문복사신청을 하시면, 일부 해외 인쇄학술지의 경우 외국학술지지원센터(FRIC)에서
무료 원문복사 서비스를 제공합니다.

NDSL에서는 해당 원문을 복사서비스하고 있습니다. 위의 원문복사신청 또는 장바구니 담기를 통하여 원문복사서비스 이용이 가능합니다.

이 논문과 함께 출판된 논문 + 더보기