10 citations · 21 across the 15 of their papers we have counts for
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Asymptotic behaviors of fractional binomial distributions derived from the generalized binomial theorem
Masanori Hino, Ryuya Namba
A fractional binomial distribution, introduced by Hino and Namba (2024) via the generalized binomial theorem, is a fractional variant of the classical binomial distribution. Buildi…
On some properties of a positive linear operator via the Moran model in population genetics
Takahiro Aoyama, Ryuya Namba
We introduce a positive linear operator acting on the Banach space of all continuous functions on the unit interval via the Moran model studied in population genetics. We show that…
Fractional binomial distributions induced by the generalized binomial theorem and their applications
Masanori Hino, Ryuya Namba
We develop a fractional extension of the classical binomial distribution and the associated Bernstein operator, formulated within the framework of the generalized binomial theorem…
Iterates of multidimensional Bernstein-type operators and diffusion processes in population genetics
Takatoshi Hirano, Ryuya Namba
The Bernstein operator is known as a typical example of positive linear operators which uniformly approximates continuous functions on . In the present paper, we introduce…
Limit theorems for iterates of the Szász-Mirakyan operator in probabilistic view
Jirô Akahori, Ryuya Namba, Shunsuke Semba
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…
Random walks on crystal lattices and multiple zeta functions
Takahiro Aoyama, Ryuya Namba
Crystal lattices are known to be one of the generalizations of classical periodic lattices which can be embedded into some Euclidean spaces properly. As to make a wide range of mul…
Asymptotic behaviors of convolution powers of the Riemann zeta distribution
Takahiro Aoyama, Ryuya Namba, Koki Ota
In probability theory, there exist discrete and continuous distributions. Generally speaking, we do not have sufficient kinds and properties of discrete ones compared to the contin…
Edgeworth expansions for centered random walks on covering graphs of polynomial volume growth
Ryuya Namba
Edgeworth expansions for random walks on covering graphs with groups of polynomial volume growths are obtained under a few natural assumptions. The coefficients appearing in this e…
Laws of the iterated logarithm on covering graphs with groups of polynomial volume growth
Ryuya Namba
Moderate deviation principles (MDPs) for random walks on covering graphs with groups of polynomial volume growth are discussed in a geometric point of view. They deal with any inte…
Central limit theorems for non-symmetric random walks on nilpotent covering graphs: Part II
Satoshi Ishiwata, Hiroshi Kawabi, Ryuya Namba
In the present paper, as a continuation of our preceding paper [10], we study another kind of central limit theorems (CLTs) for non-symmetric random walks on nilpotent covering gra…
Central limit theorems for non-symmetric random walks on nilpotent covering graphs: Part I
Satoshi Ishiwata, Hiroshi Kawabi, Ryuya Namba
In the present paper, we study central limit theorems (CLTs) for non-symmetric random walks on nilpotent covering graphs from a point of view of discrete geometric analysis develop…
A remark on a central limit theorem for non-symmetric random walks on crystal lattices
Ryuya Namba
Recently, Ishiwata, Kawabi and Kotani [2] proved two kinds of central limit theorems for non-symmetric random walks on crystal lattices from the view point of discrete geometric an…