Limit Theorems for Iterates of the Szasz-Mirakyan Operator in Probabilistic View
Limit Theorems for Iterates of the Szasz-Mirakyan Operator in Probabilistic View
复制标题
概率视角下Szasz-Mirakyan算子迭代的极限定理
DOI：
10.1007/s10959-022-01199-5
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发表时间：
2022
影响因子：
0.8
通讯作者：
Semba Shunsuke
中科院分区：
文献类型：
--
作者：
Akahori Jiro;Namba Ryuya;Semba Shunsuke
Szász-Mirakyan算子被称为正线性算子，它一致逼近半直线上的某类连续函数。本文的目的是从概率的角度来研究Szász-Mirakyan算子迭代的极限行为。我们证明了Szász-Mirakyan算子的迭代一致收敛于由二阶退化微分算子生成的连续半群.的概率解释的收敛性的离散马尔可夫链构造的迭代和半线上的限制扩散过程中捕获。
The Szász–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 Szász–Mirakyan operator in a probabilistic point of view. We show that the iterates of the Szász–Mirakyan operator uniformly converge 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.