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2013•Journal of the Korea Society of Computer and InformationOpen access

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

Sung Hee Choi, Suk-Hyung Hwang

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Abstract

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.

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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.

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Available abstract

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.

Key concepts: Classical Wiener space, Integral representation theorem for classical Wiener space, Linear subspace, Wiener process, Subspace topology, Mathematics, Fold (higher-order function), Dimension (graph theory)

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