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

Hyun-Suk Park ()
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Hyun-Suk Park: Division of Data Science, Data Science Convergence Research Center, Hallym University, Chuncheon 24252, Republic of Korea

Mathematics, 2025, vol. 13, issue 2, 1-15

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.

Keywords: Malliavin calculus; Stein’s method; density function; standard normal random variable; Itô diffusion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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