Toshihisa Ozawa

activity

20122025

most citedExact asymptotic formulae of the stationary distribution of a discrete-time 2d-QBD process: an example and additional proofs

1 citations · 3 across the 11 of their papers we have counts for

collaborators

11 papers

math.PR2025

Asymptotics of the occupation measure defined on a nonnegative matrix of two-dimensional quasi-birth-and-death type

Toshihisa Ozawa

We consider a nonnegative matrix having the same block structure as that of the transition probability matrix of a two-dimensional quasi-birth-and-death process (2d-QBD process for…

math.PR2023★ 1 cited

Exact asymptotics of the stationary tail probabilities in an arbitrary direction in a two-dimensional discrete-time QBD process

Toshihisa Ozawa

We deal with a discrete-time two-dimensional quasi-birth-and-death process (2d-QBD process for short) on $Z_{+}^{2} \times S_{0}$ , where $S_{0}$ is a finite set, and give a complet…

math.PR2022

Tail Asymptotics in any direction of the stationary distribution in a two-dimensional discrete-time QBD process

Toshihisa Ozawa

We consider a discrete-time two-dimensional quasi-birth-and-death process (2d-QBD process for short) ${(X_{n}, J_{n})}$ on $Z_{+}^{2} \times S_{0}$ , where $\boldsymbol{…

math.PR2020

Asymptotic property of the occupation measures in a multi-dimensional skip-free Markov modulated random walk

Toshihisa Ozawa

We consider a discrete-time $d$ -dimensional process ${X_{n}} = {(X_{1, n}, X_{2, n}, ..., X_{d, n})}$ on $Z^{d}$ with a background process ${J_{n}}$ on a countable se…

math.PR2020

Asymptotic property of the occupation measures in a two-dimensional skip-free Markov modulated random walk

Toshihisa Ozawa

We consider a discrete-time two-dimensional process ${(X_{1, n}, X_{2, n})}$ on $Z^{2}$ with a background process ${J_{n}}$ on a finite set $S_{0}$ , where individual processes…

math.PR2018

Stability condition of a two-dimensional QBD process and its application to estimation of efficiency for two-queue models

Toshihisa Ozawa

In order to analyze stability of a two-queue model, we consider a two-dimensional quasi-birth-and-death process (2d-QBD process), denoted by $\{\boldsymbol{Y}(t)\}=\{((L_1(t),L_2(t…

math.PR2018★ 1 cited

Exact asymptotic formulae of the stationary distribution of a discrete-time 2d-QBD process: an example and additional proofs

Toshihisa Ozawa, Masahiro Kobayashi

A discrete-time two-dimensional quasi-birth-and-death process (2d-QBD process), ${Y_{n}} = {(X_{1, n}, X_{2, n}, J_{n})}$ , is a two-dimensional skip-free random walk $\{(X_{…

math.PR2017

Exact asymptotic formulae of the stationary distribution of a discrete-time two-dimensional QBD process

Toshihisa Ozawa, Masahiro Kobayashi

We consider a discrete-time two-dimensional process ${(L_{1, n}, L_{2, n})}$ on $Z_{+}^{2}$ with a supplemental process ${J_{n}}$ on a finite set, where individual processes $\…

math.PR2016

Convergence parameters of nonnegative block tri-diagonal matrices and their application to multi-dimensional QBD processes

Toshihisa Ozawa

First, we consider a nonnegative homogeneous block tri-diagonal matrix and obtain its convergence parameter, where some results in the field of matrix analytic method are extended…

math.PR2013★ 1 cited

Positive recurrence and transience of a two-station network with server states

Toshihisa Ozawa

We study positive recurrence and transience of a two-station network in which the behavior of the server in each station is governed by a Markov chain with a finite number of serve…

math.PR2012

Stability of multidimensional skip-free Markov modulated reflecting random walks: Revisit to Malyshev and Menshikov's results and application to queueing networks

Toshihisa Ozawa

Let ${X_{n}}$ be a discrete-time $d$ -dimensional process on $Z_{+}^{d}$ with a supplemental (background) process ${J_{n}}$ on a finite set and assume the joint pr…