论文标题
在概率上限制Szász-Mirakyan操作员的迭代定理
Limit theorems for iterates of the Szász-Mirakyan operator in probabilistic view
论文作者
论文摘要
Szász-Mirakyan操作员被称为正线性算子，在半线上均匀地近似一类连续函数。本文的目的是找出Szász-Mirakyan操作员的局限性行为。我们表明，szász-mirakyan操作员的迭代均匀地收敛到由二阶退化差分算子产生的连续半群。也捕获了从迭代元素构建的离散马尔可夫链和半线上的限制扩散过程的概率解释。
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 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.
