Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지

ANALOGUE OF WIENER MEASURE OVER THE SETS BOUNDED BY SECTIONALLY DIFFERENTIABLE BARRIERS

  • Im, Man Kyu (Department of Mathematics HanNam University)
  • Received : 2009.12.09
  • Accepted : 2010.02.18
  • Published : 2010.03.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we find the formula for the analogue of Wiener measure over the subset of C[0, T] bounded by the sectionally differentiable functions, which is a generalization of Park and Skoug's results in [2].

Keywords

References

  1. C. Park and S. R. Paranjape, Probabilities of Wiener paths crossing differentable curves, Pacific J. Math. 53 (1974), 579-583. https://doi.org/10.2140/pjm.1974.53.579
  2. C. Park and D. L. Skoug, Wiener integrals over the sets bounded by sectionally continuous barriers, Pacific J. Math. 66 (1976), 523-534. https://doi.org/10.2140/pjm.1976.66.523
  3. 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
  4. K. S. Ryu, Probabilities of analogue of Wiener paths crossing continuously differentiable curves, J. Chungcheong Math. Soc. 22 (2009), 579-586.
  5. S. Saks, Theory of the integral, Hafner, 1936.
  6. L. A. Shepp, Radon-Nikodym derivatives of Gaussian measures, Ann. Math. Stat. 37 (1966), 321-354. https://doi.org/10.1214/aoms/1177699516
  7. H. G. Tucker, A graduate course in probability, Academic press, New York, 1967.
  8. F. G. Tricomi, Integral Equations, Interscience Publishers, Inc., 1957.