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An Approximation Scheme for Diffusion Processes Based on an Antisymmetric Calculus over Wiener Space

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Abstract

In this paper, we show that every antisymmetric multiple stochastic (Ito’s) integral has a polynomial form of single and double ones. As an application, a new approximating scheme for the solution to a stochastic differential equation is proposed.

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Acknowledgments

The author would like to express sincere appreciations to Professor Jirô Akahori for his valuable comments. This work was partially supported by JSPS KAKENHI Grant Numbers 23654056 and 25285102.

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Authors and Affiliations

  1. Graduate School of Science and Engineering, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga, 525-8577, Japan

    Kazuhiro Yoshikawa

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  1. Kazuhiro Yoshikawa
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Correspondence to Kazuhiro Yoshikawa.

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Yoshikawa, K. An Approximation Scheme for Diffusion Processes Based on an Antisymmetric Calculus over Wiener Space. Asia-Pac Financ Markets 22, 185–207 (2015). https://doi.org/10.1007/s10690-014-9199-2

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  • DOI: https://doi.org/10.1007/s10690-014-9199-2

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