TITLE:
Extended Wiener Measure by Nonstandard Analysis for Financial Time Series
AUTHORS:
Shuya Kanagawa, Ryoukichi Nishiyama, Kiyoyuki Tchizawa
KEYWORDS:
Time Series, Black-Sholes Model, S-Continuity, Nonstandard Analysis, Delta-Function
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.8,
August
30,
2018
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.