Density Formula in Malliavin Calculus by Using Stein’s Method and Diffusions
Let <i>G</i> be a random variable of functionals of an isonormal Gaussian process <i>X</i> defined on some probability space. Studies have been conducted to determine the exact form of the density function of the random variable <i>G</i>. In this paper, unlike pre...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/2/323 |
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| Summary: | Let <i>G</i> be a random variable of functionals of an isonormal Gaussian process <i>X</i> defined on some probability space. Studies have been conducted to determine the exact form of the density function of the random variable <i>G</i>. In this paper, unlike previous studies, we will use the Stein’s method for invariant measures of diffusions to obtain the density formula of <i>G</i>. 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. |
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| ISSN: | 2227-7390 |