Hiroshi Ishitani

Hiroshi Ishitani
Mie University · Faculty of Education

Doctor of Science (Hiroshima University)

About

18
Publications
616
Reads
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77
Citations
Additional affiliations
April 2013 - December 2016
Mie University
Position
  • Professor Emeritus
April 1991 - March 2013
Mie University
Position
  • Professor
November 1985 - August 1986
Friedrich-Alexander-University of Erlangen-Nürnberg
Position
  • Guest Professor
Education
April 1973 - March 1974
Kyoto University
Field of study
  • Ph.D. Course in Department of Mathematics, Graduate School of Science
April 1971 - March 1973
Kyoto University
Field of study
  • Master Course in Department of Mathematics, Graduate School of Science
April 1966 - March 1971
Kyoto University
Field of study
  • Faculty of Science

Publications

Publications (18)
Article
It is known that the Perron--Frobenius operators of piecewise expanding $\mathcal{C}^2$ transformations possess an asymptotic periodicity of densities. On the other hand, external noise or measurement errors are unavoidable in practical systems; therefore, all realistic mathematical models should be regarded as random iterations of transformations....
Article
It is known that the Perron-Frobenius operators of piecewise expanding C² transformations have an asymptotic periodicity of densities. On the other hand, external noise or measurement errors are unavoidable in practical systems, and therefore, every realistic mathematical model should be regarded as random iterations of transformations. The aim of...
Article
Full-text available
This paper is concerned with invariant densities for transformations on R which are the boundary restrictions of inner functions of the upper half plane. G. Letac [9] proved that if the corresponding inner function has a fixed point z0 in C\R or a periodic point z0 in C\R with period 2, then a Cauchy distribution (1/π)Im (1/(x - z0)) is an invarian...
Article
Full-text available
This paper is concerned with giving explicitly the invariant density for a class of rational transformations from the realline R into itself. We proved that the invariant density can be written in terms of the fixed point z0 in C/R or in terms of the periodic point z0 in C/R with period 2. The explicit from of the density allows us to obtain the er...
Article
In this article, we considered the asymptotic expectations of the prediction error and the fitting error of a regression model, in which the component functions are chosen from a finite set of orthogonal functions. Under the least squares estimation, we showed that the asymptotic bias in estimating the prediction error based on the fitting error in...
Article
The study of dynamical systems (Kyoto, 1989) ed. N. Aoki World Scientific Advanced Series in Dynamical Systems 7 122--139 World Sci. Publ. 1989
Article
Full-text available
The purpose of the present paper is to give central limit theorems for piecewise linear transformations ([6]), which are generalizations of /^-transformations and which belong to a class of number-theoretical transformations with "dependent digits" (cf. [4]). The central limit theorems for ones with "independent digits" are studied by many authors...

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