Proof of Ito’s Formula for Ito’s Process in Nonstandard Analysis

HTML  XML Download Download as PDF (Size: 247KB)  PP. 561-567  
DOI: 10.4236/am.2019.107039    948 Downloads   1,807 Views  Citations

ABSTRACT

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.

Share and Cite:

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.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.