DOI QR코드

DOI QR Code

THE SIMPLE FORMULA OF CONDITIONAL EXPECTATION ON ANALOGUE OF WIENER MEASURE

  • Ryu, Kun-Sik (Department of Mathematics Education, Han Nam University)
  • Received : 2008.10.30
  • Accepted : 2008.12.04
  • Published : 2008.12.25

Abstract

In this note, we establish the uniqueness theorem of conditional expectation on analogue of Wiener measure space for given distributions and prove the simple formula of conditional expectation on analogue of Wiener measure which is essentially similar to Park and Skoug's formula on the concrete Wiener measure.

Keywords

References

  1. P. R. Halmos, Measure theory, Springer-Verlag, New York (1971).
  2. M. K. Im and K. S. Ryu, An analogue of Wiener measure and its applications, J. Korean Math. Soc. 39 (2002), pp. 801-819. https://doi.org/10.4134/JKMS.2002.39.5.801
  3. C. Park and D. L. Skoug, A simple formula for conditional Wiener integrals with applications, Pacific J. Math. 135 (1988), pp. 381-394. https://doi.org/10.2140/pjm.1988.135.381
  4. K. R. Parthasarathy, Probability measures on metric spaces, Academic Press, New York, 1967.
  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. 354 (2002), pp. 4921-4951. https://doi.org/10.1090/S0002-9947-02-03077-5
  6. K. S. Ryu and M.K. Im, The measure-valued Dyson series and its stability theorem, J. Korean Math. Soc. 43 (2006), pp. 461-489. https://doi.org/10.4134/JKMS.2006.43.3.461
  7. H. G. Tucker, A graduate course in probability, Academic press, New York (1967).
  8. N. Wiener, Differential space, J. Math. Phys. 2 (1923). pp. 131-174. https://doi.org/10.1002/sapm192321131
  9. J. Yeh, Inversion of conditional expectations, Pacific J. Math., 52 (1974), pp. 631-640. https://doi.org/10.2140/pjm.1974.52.631

Cited by

  1. Survey of the Theories for Analogue of Wiener Measure Space vol.15, pp.3, 2009, https://doi.org/10.4036/iis.2009.319