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Density Formula in Malliavin Calculus by Using Stein’s Method and Diffusions

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  • Hyun-Suk Park

    (Division of Data Science, Data Science Convergence Research Center, Hallym University, Chuncheon 24252, Republic of Korea)

Abstract

Let G be a random variable of functionals of an isonormal Gaussian process X defined on some probability space. Studies have been conducted to determine the exact form of the density function of the random variable G . In this paper, unlike previous studies, we will use the Stein’s method for invariant measures of diffusions to obtain the density formula of G . By comparing the density function obtained in this paper with that of the diffusion invariant measure, we find that the diffusion coefficient of an Itô diffusion with an invariant measure having a density can be expressed as in terms of operators in Malliavin calculus.

Suggested Citation

  • Hyun-Suk Park, 2025. "Density Formula in Malliavin Calculus by Using Stein’s Method and Diffusions," Mathematics, MDPI, vol. 13(2), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:323-:d:1571356
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    References listed on IDEAS

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    1. Kusuoka, Seiichiro & Tudor, Ciprian A., 2012. "Stein’s method for invariant measures of diffusions via Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1627-1651.
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