On the Transition Density of the Time-Inhomogeneous 3/2 Model: A Unified Approach for Models Related to Squared Bessel Process
We derive an infinite-series representation for the transition probability density function (PDF) of the time-inhomogeneous 3/2 model, expressing all coefficients in terms of Bell-polynomial and generalized Laguerre-polynomial formulas. From this series, we obtain explicit expressions for all condit...
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2025-06-01
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| author | Rattiya Meesa Ratinan Boonklurb Phiraphat Sutthimat |
| author_facet | Rattiya Meesa Ratinan Boonklurb Phiraphat Sutthimat |
| author_sort | Rattiya Meesa |
| collection | DOAJ |
| description | We derive an infinite-series representation for the transition probability density function (PDF) of the time-inhomogeneous 3/2 model, expressing all coefficients in terms of Bell-polynomial and generalized Laguerre-polynomial formulas. From this series, we obtain explicit expressions for all conditional moments of the variance process, recovering the familiar time-homogeneous formulas when parameters are constant. Numerical experiments illustrate that both the density and moment series converge rapidly, and the resulting distributions agree with high-precision Monte Carlo simulations. Finally, we demonstrate that the same approach extends to a broad family of non-affine, time-varying diffusions, providing a general framework for obtaining transition PDFs and moments in advanced models. |
| format | Article |
| id | doaj-art-4af4a76b33b2425fbb69136acdf4406a |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-4af4a76b33b2425fbb69136acdf4406a2025-08-20T03:27:40ZengMDPI AGMathematics2227-73902025-06-011312194810.3390/math13121948On the Transition Density of the Time-Inhomogeneous 3/2 Model: A Unified Approach for Models Related to Squared Bessel ProcessRattiya Meesa0Ratinan Boonklurb1Phiraphat Sutthimat2Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, ThailandDepartment of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, ThailandDepartment of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, ThailandWe derive an infinite-series representation for the transition probability density function (PDF) of the time-inhomogeneous 3/2 model, expressing all coefficients in terms of Bell-polynomial and generalized Laguerre-polynomial formulas. From this series, we obtain explicit expressions for all conditional moments of the variance process, recovering the familiar time-homogeneous formulas when parameters are constant. Numerical experiments illustrate that both the density and moment series converge rapidly, and the resulting distributions agree with high-precision Monte Carlo simulations. Finally, we demonstrate that the same approach extends to a broad family of non-affine, time-varying diffusions, providing a general framework for obtaining transition PDFs and moments in advanced models.https://www.mdpi.com/2227-7390/13/12/1948characteristic function3/2 modelnoncentral Chi-squaresquared Bessel processtransition density function |
| spellingShingle | Rattiya Meesa Ratinan Boonklurb Phiraphat Sutthimat On the Transition Density of the Time-Inhomogeneous 3/2 Model: A Unified Approach for Models Related to Squared Bessel Process Mathematics characteristic function 3/2 model noncentral Chi-square squared Bessel process transition density function |
| title | On the Transition Density of the Time-Inhomogeneous 3/2 Model: A Unified Approach for Models Related to Squared Bessel Process |
| title_full | On the Transition Density of the Time-Inhomogeneous 3/2 Model: A Unified Approach for Models Related to Squared Bessel Process |
| title_fullStr | On the Transition Density of the Time-Inhomogeneous 3/2 Model: A Unified Approach for Models Related to Squared Bessel Process |
| title_full_unstemmed | On the Transition Density of the Time-Inhomogeneous 3/2 Model: A Unified Approach for Models Related to Squared Bessel Process |
| title_short | On the Transition Density of the Time-Inhomogeneous 3/2 Model: A Unified Approach for Models Related to Squared Bessel Process |
| title_sort | on the transition density of the time inhomogeneous 3 2 model a unified approach for models related to squared bessel process |
| topic | characteristic function 3/2 model noncentral Chi-square squared Bessel process transition density function |
| url | https://www.mdpi.com/2227-7390/13/12/1948 |
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