Limit theorems for iterates of the Sz\'asz-Mirakyan operator in probabilistic view
| العنوان: | Limit theorems for iterates of the Sz\'asz-Mirakyan operator in probabilistic view |
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| المؤلفون: | Jirô Akahori, Ryuya Namba, Shunsuke Semba |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | Statistics and Probability, Mathematics - Functional Analysis, General Mathematics, Statistics, Probability and Uncertainty, Mathematics - Probability, Primary 60J10, 60J60, Secondary 41A25, 41A36, 47D03 |
| الوصف: | The Sz\'asz-Mirakyan operator is known as a positive linear operator which uniformly approximates a certain class of continuous functions on the half line. The purpose of the present paper is to find out limiting behaviors of the iterates of the Sz\'asz-Mirakyan operator in a probabilistic point of view. We show that the iterates of the Sz\'asz-Mirakyan operator uniformly converges to a continuous semigroup generated by a second order degenerate differential operator. A probabilistic interpretation of the convergence in terms of a discrete Markov chain constructed from the iterates and a limiting diffusion process on the half line is captured as well. Comment: 17 pages |
| اللغة: | English |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a9aa0c2f90771c0e107e925066da0337 http://arxiv.org/abs/2207.06756 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....a9aa0c2f90771c0e107e925066da0337 |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |