Factorial moments of the critical Markov branching process with geometric reproduction of particles
The factorial moments of any Markov branching process describe the behaviour of its probability generating function $F(t,s)$ in the neighbourhood of the point $s=1$. They are applied to solve the forward Kolmogorov equation for the critical Markov branching process with geometric reproduction of par...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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VTeX
2022-02-01
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| Series: | Modern Stochastics: Theory and Applications |
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| Online Access: | https://www.vmsta.org/doi/10.15559/22-VMSTA201 |
| _version_ | 1818201054069653504 |
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| author | Assen Tchorbadjieff Penka Mayster |
| author_facet | Assen Tchorbadjieff Penka Mayster |
| author_sort | Assen Tchorbadjieff |
| collection | DOAJ |
| description | The factorial moments of any Markov branching process describe the behaviour of its probability generating function $F(t,s)$ in the neighbourhood of the point $s=1$. They are applied to solve the forward Kolmogorov equation for the critical Markov branching process with geometric reproduction of particles. The solution includes quickly convergent recurrent iterations of polynomials. The obtained results on factorial moments enable computation of statistical measures as shape and skewness. They are also applicable to the comparison between critical geometric branching and linear birth-death processes. |
| first_indexed | 2024-12-12T02:47:27Z |
| format | Article |
| id | doaj.art-4b0b0a14f5394ab6a329ffa902298ad9 |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2024-12-12T02:47:27Z |
| publishDate | 2022-02-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-4b0b0a14f5394ab6a329ffa902298ad92022-12-22T00:40:58ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542022-02-019222924410.15559/22-VMSTA201Factorial moments of the critical Markov branching process with geometric reproduction of particlesAssen Tchorbadjieff0Penka Mayster1Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev street, Bloc 8, 1113 Sofia, BulgariaInstitute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev street, Bloc 8, 1113 Sofia, BulgariaThe factorial moments of any Markov branching process describe the behaviour of its probability generating function $F(t,s)$ in the neighbourhood of the point $s=1$. They are applied to solve the forward Kolmogorov equation for the critical Markov branching process with geometric reproduction of particles. The solution includes quickly convergent recurrent iterations of polynomials. The obtained results on factorial moments enable computation of statistical measures as shape and skewness. They are also applicable to the comparison between critical geometric branching and linear birth-death processes.https://www.vmsta.org/doi/10.15559/22-VMSTA201factorial momentsgeometric reproduction branching processharmonic numbersLambert-W functionStirling numbers |
| spellingShingle | Assen Tchorbadjieff Penka Mayster Factorial moments of the critical Markov branching process with geometric reproduction of particles Modern Stochastics: Theory and Applications factorial moments geometric reproduction branching process harmonic numbers Lambert-W function Stirling numbers |
| title | Factorial moments of the critical Markov branching process with geometric reproduction of particles |
| title_full | Factorial moments of the critical Markov branching process with geometric reproduction of particles |
| title_fullStr | Factorial moments of the critical Markov branching process with geometric reproduction of particles |
| title_full_unstemmed | Factorial moments of the critical Markov branching process with geometric reproduction of particles |
| title_short | Factorial moments of the critical Markov branching process with geometric reproduction of particles |
| title_sort | factorial moments of the critical markov branching process with geometric reproduction of particles |
| topic | factorial moments geometric reproduction branching process harmonic numbers Lambert-W function Stirling numbers |
| url | https://www.vmsta.org/doi/10.15559/22-VMSTA201 |
| work_keys_str_mv | AT assentchorbadjieff factorialmomentsofthecriticalmarkovbranchingprocesswithgeometricreproductionofparticles AT penkamayster factorialmomentsofthecriticalmarkovbranchingprocesswithgeometricreproductionofparticles |