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Kouji Yano

Publications and source records attributed to Kouji Yano.

At least 19 recordsLinked to original sources
arXiv2026

The Law of Large Numbers for Time-inhomogeneous Markov Chains under General Conditions

The weak and strong laws of large numbers for time-inhomogeneous Markov chains are studied under general conditions. First, under Drift Condition and Contraction Condition in total variation, we prove the weak law of large numbers. Then, assuming Drift Condition together with a time-inhomogeneous Doeblin minorization, we develop a Nummelin-type splitting and obtain a strong law of large numbers. Our results utilize the invariant measure family in the sense of Liu--Lu (2025), and extend the classical Harris-ergodic LLN to the time-inhomogeneous setting.

math.PR↗
arXiv2025

Limit theorems for the fluctuation of the dynamic elephant random walk in the superdiffusive case

Motivated by the previous results by Coletti-de Lima-Gava-Luiz (2020) and Shiozawa (2022), we study the fluctuation of the dynamic elephant random walk in the superdiffusive case with a strong elephant component. Applying the martingale convergence theorem, we prove the Central Limit Theorem and the Law of Iterated Logarithm, where a random drift is subtracted from the process considered.

math.PR↗
arXiv2023

A cluster representation of the renewal Hawkes process

A cluster representation for a Hawkes process with renewal immigration is obtained. The centre and satellite processes are indicated as a renewal process and generalized branching processes respectively. It is confirmed that the proposed construction indeed represents a cluster process and it is verified that it admits the desired intensity. Finally, the probability generating functional is computed for the stationary limit case.

math.PR↗
arXiv2022

Arcsine law for random dynamics with a core

In their recent paper [8], G.Hata and the fourth author first gave an example of random iterations of two piecewise linear interval maps without (deterministic) indifferent periodic points for which the arcsine law -- a characterization of intermittent dynamics in infinite ergodic theory -- holds. The key in the proof of the result is the existence of a Markov partition preserved by each interval maps. In the present paper, we give a class of random iterations of two interval maps without indifferent periodic points but satisfying the arcsine law, by introducing a concept of core random dynamics. As applications, we show that the generalized arcsine law holds for generalized Hata-Yano maps and piecewise linear versions of Gharaei-Homburg maps, both of which do not have a Markov partition in general.

math.DS↗
arXiv2022

Reproduction of initial distributions from the first hitting time distribution for birth-and-death processes

For birth-and-death processes, we show that every initial distribution is reproduced from the first hitting time distribution. The reproduction is done by applying to the distribution function a differential operator defined through the eigenfunction of the generator. Using the spectral theory for generalized second-order differential operators, we study asymmetric random walks.

math.PR↗
arXiv2022

Local time penalizations with various clocks for L\'{e}vy processes

Several long-time limit theorems of one-dimensional L\'{e}vy processes weighted and normalized by functions of the local time are studied. The long-time limits are taken via certain families of random times, called clocks: exponential clock, hitting time clock, two-point hitting time clock and inverse local time clock. The limit measure can be characterized via a certain martingale expressed by an invariant function for the process killed upon hitting zero. The limit processes may differ according to the choice of the clocks when the original L\'{e}vy process is recurrent and of finite variance.

math.PR↗
arXiv2021

Infinite convolutions of probability measures on Polish semigroups

This expository paper is intended for a short self-contained introduction to the theory of infinite convolutions of probability measures on Polish semigroups. We give the proofs of the Rees decomposition theorem of completely simple semigroups, the Ellis--Żelazko theorem, the convolution factorization theorem of convolution idempotents, and the convolution factorization theorem of cluster points of infinite convolutions.

math.PR↗
arXiv2021

Arcsine and Darling--Kac laws for piecewise linear random interval maps

We give examples of piecewise linear random interval maps satisfying arcsine and Darling--Kac laws, which are analogous to Thaler's arcsine and Aaronson's Darling--Kac laws for the Boole transform. They are constructed by random switch of two piecewise linear maps with attracting or repelling fixed points, which behave as if they were indifferent fixed points of a deterministic map.

math.DS↗
arXiv2020

Remarks on martingale representation theorem for set-valued martingales

Martingale representation theorem for set-valued martingales was proposed by M. Kisielewicz [J. Math. Anal. Appl. 2014]. We shall prove that the result holds only for very special case: the set-valued martingale degenerates to the point-valued one. A revised representation theorem for a special kind of non-degenerate set-valued martingales is presented.

math.PR↗
arXiv2020

Aging arcsine law in Brownian motion and its generalization

Classical arcsine law states that fraction of occupation time on the positive or the negative side in Brownian motion does not converge to a constant but converges in distribution to the arcsine distribution. Here, we consider how a preparation of the system affects the arcsine law, i.e., aging of the arcsine law. We derive aging distributional theorem for occupation time statistics in Brownian motion, where the ratio of time when measurements start to the measurement time plays an important role in determining the shape of the distribution. Furthermore, we show that this result can be generalized as aging distributional limit theorem in renewal processes.

math.PR↗
arXiv2019

Generalized refracted Lévy process and its application to exit problem

Generalizing Kyprianou--Loeffen's refracted Lévy processes, we define a new refracted Lévy process which is a Markov process whose positive and negative motions are Lévy processes different from each other. To construct it we utilize the excursion theory. We study its exit problem and the potential measures of the killed processes. We also discuss approximation problem.

math.PR↗