충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제27권4호
  • /
  • Pages.689-695
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  • 2014
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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THE ANALOGUE OF WIENER SPACE WITH VALUES IN ORLICZ SPACE

  • Ryu, Kun Sik (Department of Mathematics Education Hannam University)
  • 투고 : 2014.09.17
  • 심사 : 2014.10.20
  • 발행 : 2014.11.15
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초록

Let M be an N-function satisfies the ${\Delta}_2$-condition and let $O_M$ be the Orlicz space associated with M. Let $C(O_M)$ be the space of all continuous functions defined on the interval [0, T] with values in $O_M$. In this note, we define the analogue of Wiener measure $m^M_{\phi}$ on $C(O_M)$, establish the Wiener integration formulae for the cylinder functions on $C(O_M)$ and give some examples related to our formulae.

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참고문헌

  1. T. Byczkowski, Gaussian Measures on Lp Spaces, 0 < p < ${\infty}$, Studia Math. 59 (1977), no. 2, 299-313.
  2. L. Gross, Abstract Wiener Spaces, Pro. Fifth Berkeley Sympos. Math. Statist and Probability(Berkeley), Calif.(1965/66), Vol. II:Contributions to Probability Theory, Part I, pp 31-42, Univ. Califonia Press, Berkeley, Calif., 1967.
  3. Abdallah Hakawati, The Multiplier Algebra of Orlicz Spaces, An-Nahaj Univ. J, Res. 12 (1998), 1-6.
  4. T. Jurlewicz, Law of the Iterated Logarithm for Wiener Processes with Values in Orlicz Spaces, Probability and Mathematical Statistics 7 (1986), 159-167.
  5. M. A. Kransnoselskii and Ya. B. Rutickii, Convex Functions and Orlicz Spaces, P. Nororodhoff, Ltd. Groningen, 1961.
  6. J. Kuelbs and R. LaPage, The law of the Iterated Logarithm for Brownian Motion in a Banach space, Trans. Amer. Math. Soc. 185 (1973), 253-264. https://doi.org/10.1090/S0002-9947-1973-0370725-3
  7. A. Lawniczak, Gaussian Measures on Orlicz Spaces and Abstract Wiener Spaces, Lecture Notes in Math. 939 (1982), 81-97.
  8. B. Rajput, Gaussian Measures on $L_p$ spaces, $1{\leq}p{\leq}{\infty}$, Multivarite Analysis 2 (1972), 382-403. https://doi.org/10.1016/0047-259X(72)90034-6
  9. K. S. Ryu, The Wiener Integral over Paths in Abstract Wiener Spaces, J. Korean Math. Soc. 29 (1992), 317-331.
  10. K. S. Ryu, Integration with respect to Analogue of Wiener Measure over Paths in Abstract Wiener Space and its Applications, Bull. Korean Math. Soc. 47 (2010), 131-149. https://doi.org/10.4134/BKMS.2010.47.1.131
  11. K. S. Ryu and M. K. Im, A measure-Valued Analogue of Wiener Measure and the Measure-Valued Feynman-Kac Formula, Trans. Amer. Math. Soc. 354 (2002), 4921-4951. https://doi.org/10.1090/S0002-9947-02-03077-5
  12. N. Wiener, Differential Space, J. Math. (1923), 131-174.

피인용 문헌

  1. A NOTE ON ANALOGUE OF WIENER SPACE WITH VALUES IN ORLICZ SPACE vol.37, pp.4, 2015, https://doi.org/10.5831/HMJ.2015.37.4.505