DOI QR코드

DOI QR Code

r-fold Wiener process에 대한 유한근사함수의 특성에 관한 연구

A study on the properties of the finite-dimensional approximation of an r-fold Wiener Process

  • 투고 : 2012.12.27
  • 심사 : 2013.02.23
  • 발행 : 2013.03.30

초록

r-fold Wiener process는 실질적으로 infinite dimension이고, 컴퓨터는 finitely dimensional subspace만 취급할 수 있기 때문에 f-fold Wiener process는 컴퓨터로 구현될 수 없다. 따라서 본 논문에서는 r-fold Wiener process의 m-dimensional approximation 함수의 특성에 대해 연구한다.

Because the r-fold Wiener process is truly infinitely dimensional and a computer can only handle finitely dimensional subspaces, we study in this paper the basic properties of the m-dimensional approximation function of the r-fold Wiener process.

키워드

참고문헌

  1. S. Choi and B. Hong, "An Effor of Simpson's Quadrature in the Average Case Setting," J. of Korean Math. Soc. 33 (1996), 235-247.
  2. H. H. Kuo, "Gaussian Measures in Banach Spaces," Lecture Notes in Mathematics 463, Springer-Verlag, Berlin, 1975.
  3. L. Plaskota, "Average Approximation and Integration in the Wiener Space with Noisy Data," J. of Complexity 8 (1992), 301-323. https://doi.org/10.1016/0885-064X(92)90028-A
  4. K. Ritter, G. W. Wasilkowski, and H. Wozniakowski, "On Multivariage Integration for Stochastic Processes," International Series of Numerical Mathematics 112 (1993), 331-347.
  5. J. F. Traub, G. W. Wasilkowski, and H. Wozniakowski, "Information-Based Complexity," Academic Press, New York, 1988.