Entropies of Cox-Ingersoll-Ross and Bessel processes as functions of time and of related parameters
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911066618855424 |
|---|---|
| author | Kucha, Ivan Mishura, Yuliya Ralchenko, Kostiantyn |
| author_facet | Kucha, Ivan Mishura, Yuliya Ralchenko, Kostiantyn |
| contents | We investigate the long-time asymptotic behavior of various entropy measures associated with the Cox-Ingersoll-Ross (CIR) and squared Bessel processes. As the one-dimensional distributions of both processes follow noncentral chi-squared laws, we first derive sufficient conditions for the existence of these entropy measures for a noncentral chi-squared random variable. We then analyze their limiting behavior as the noncentrality parameter approaches zero and apply these results to the CIR and squared Bessel processes. We prove that, as time tends to infinity, the entropies of the CIR process converge to those of its stationary distribution, while for the squared Bessel process, the Shannon, Rényi, and generalized Rényi entropies diverge, however, the Tsallis and Sharma-Mittal entropies may diverge or remain finite depending on the entropy parameters. Finally, we demonstrate that, as the CIR process converges to the squared Bessel process, the corresponding entropies also converge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14684 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entropies of Cox-Ingersoll-Ross and Bessel processes as functions of time and of related parameters Kucha, Ivan Mishura, Yuliya Ralchenko, Kostiantyn Probability 94A17, 60E05, 60H10, 60J60 We investigate the long-time asymptotic behavior of various entropy measures associated with the Cox-Ingersoll-Ross (CIR) and squared Bessel processes. As the one-dimensional distributions of both processes follow noncentral chi-squared laws, we first derive sufficient conditions for the existence of these entropy measures for a noncentral chi-squared random variable. We then analyze their limiting behavior as the noncentrality parameter approaches zero and apply these results to the CIR and squared Bessel processes. We prove that, as time tends to infinity, the entropies of the CIR process converge to those of its stationary distribution, while for the squared Bessel process, the Shannon, Rényi, and generalized Rényi entropies diverge, however, the Tsallis and Sharma-Mittal entropies may diverge or remain finite depending on the entropy parameters. Finally, we demonstrate that, as the CIR process converges to the squared Bessel process, the corresponding entropies also converge. |
| title | Entropies of Cox-Ingersoll-Ross and Bessel processes as functions of time and of related parameters |
| topic | Probability 94A17, 60E05, 60H10, 60J60 |
| url | https://arxiv.org/abs/2507.14684 |