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Extended Wiener Measure by Nonstandard Analysis for Financial Time Series
Epartment of Mathematics, Tokyo City University, Tokyo, Japan
Department of literature, Ryukoku University, Kyoto, Japan
Institute of Administration Engineering, Ltd., Tokyo, Japan
- 1 Epartment of Mathematics, Tokyo City University, Tokyo, Japan
- 2 Department of literature, Ryukoku University, Kyoto, Japan
- 3 Institute of Administration Engineering, Ltd., Tokyo, Japan
Applied Mathematics·Volume 09 (2018)·Pages 975–984·Published 14 August 2018·DOI10.4236/am.2018.98066
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Abstract
We propose a new approach to construct an extended Wiener measure using nonstandard analysis by E. Nelson. For the new definition we construct non-standardized convolution of probability measure for independent random variables. As an application, we consider a simple calculation of financial time series.
KeywordsTime SeriesBlack-Sholes ModelS-ContinuityNonstandard AnalysisDelta-Function
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