충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제28권4호
  • /
  • Pages.615-622
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  • 2015
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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THE ARCSINE LAW IN THE ANALOGUE OF WIENER SPACE

  • Ryu, Kun Sik (Department of Mathematics Education Hannam University)
  • 투고 : 2015.09.17
  • 심사 : 2015.11.05
  • 발행 : 2015.11.15
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초록

In this note, we prove the theorems in analogue of Wiener space corresponding to the second and the third arcsine laws in the concrete Wiener space [1, 2] and we show that our results are exactly same to the concrete Wiener case when the initial condition gives the Dirac measure at the origin.

키워드

참고문헌

  1. E. Cinlar, Probability and Stochastics, Springer, 2010.
  2. I. Karatzas and S. E. Shreve, Brownian motion and Stochastic Calculus, Springer, 1998.
  3. P. Levy, Sur certaines processus stochastiques homogenes, Compos. Math. 7 (1939), 283-339.
  4. R. Durrett, Probability : Theory and Examples, 2nd edition, Duxbury Press, 1996.
  5. 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., Vol 354, 4921-4951, 2002. https://doi.org/10.1090/S0002-9947-02-03077-5

피인용 문헌

  1. An Arc-Sine Law for Last Hitting Points in the Two-Parameter Wiener Space vol.7, pp.11, 2015, https://doi.org/10.3390/math7111131