Author(s)

Shuya Kanagawa¹, Kiyoyuki Tchizawa²

¹Department of Mathematics, Tokyo City University Setagaya, Tokyo, Japan.
²Institute of Administration Engineering, Ltd., Tokyo, Japan.

In our previous paper [1], we proposed a non-standardization of the concept of convolution in order to construct an extended Wiener measure using nonstandard analysis by E. Nelson [2]. In this paper, we consider Ito’s integral with respect to the extended Wiener measure and extend Ito’s formula for Ito’s process. Because of doing the extension of Ito’s formula, we could treat stochastic differential equations in the sense of nonstandard analysis. In this framework, we need the nonstandardization of convolution again. It was not yet proved in the last paper, therefore we shall provide the proof.

Ito’s Process, Stochastic Differential Equation, S-Continuity, Nonstandard Analysis

Kanagawa, S. and Tchizawa, K. (2019) Proof of Ito’s Formula for Ito’s Process in Nonstandard Analysis. Applied Mathematics, 10, 561-567. doi: 10.4236/am.2019.107039.