Toshihisa Ozawa

activity

20172022

collaborators

6 papers

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

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 $\…