九州大学 研究者情報
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星野 壮登(ほしの まさと) データ更新日:2019.06.16



主な研究テーマ
特異な確率偏微分方程式
キーワード:ラフパス理論,正則性構造,パラ制御解析
2014.04.
研究業績
主要原著論文
1. Masato Hoshino, Global well-posedness of complex Ginzburg–Landau equation with a space–time white noise, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 54, 4, 1969-2001, 2018.11, We show the global-in-time well-posedness of the complex Ginzburg-Landau (CGL) equation with a space-time white noise on the 3-dimensional torus. Our method is based on Mourrat and Weber (Global well-posedness of the dynamic Φ43 model on the torus), where Mourrat and Weber showed the global well-posedness for the dynamical Φ43 model. We prove a priori L2p estimate for the paracontrolled solution as in the deterministic case [Phys. D 71 (1994) 285–318]..
2. Masato Hoshino, Paracontrolled calculus and Funaki-Quastel approximation for the KPZ equation, Stochastic Processes and their Applications, 128, 4, 1238-1293, 2018.04, In this paper, we consider the approximating KPZ equation introduced by Funaki and Quastel (2015), which is suitable for studying invariant measures. They showed that the stationary solution of the approximating equation converges to the Cole-Hopf solution of the KPZ equation with extra term \frac{1}{24}t. On the other hand, Gubinelli and Perkowski (2017) gave a pathwise meaning to the KPZ equation as an application of the paracontrolled calculus. We show that Funaki and Quastel's result is extended to nonstationary solutions by using the paracontrolled calculus..
3. Masato Hoshino, Yuzuru Inahama, Nobuaki Naganuma, Stochastic complex Ginzburg-Landau equation with space-time white noise, Electronic Journal of Probability, 22, 104, 2017.12.
4. Tadahisa Funaki, Masato Hoshino, A coupled KPZ equation, its two types of approximations and existence of global solutions, Journal of Functional Analysis, 273, 3, 1165-1204, 2017.08.
5. @Masato Hoshino, KPZ equation with fractional derivatives of white noise, Stochastic and Partial Differential Equations: Analysis and Computations, 4, 4, 827-890, 2016.07.
主要学会発表等
1. 星野壮登, Recovering modelled distributions from paracontrolled calculus, 確率論シンポジウム, 2018.12.
2. 星野壮登, A relation between regularity structures and paracontrolled calculus, Stochastic Analysis on Large Scale Interacting Systems, 2018.11.
3. 星野壮登, A relation between regularity structures and paracontrolled calculus, 日本数学会2018年度秋季総合分科会, 2018.09, In the world of singular SPDEs, there are two big theories: the theory of regularity structures by Hairer and the paracontrolled calculus by Gubinelli, Imkeller and Perkowski. In Hairer’s theory, the solu- tion is defined as a modeled distribution, which rep- resents a local behavior of the solution. In the GIP theory, the solution is defined as a paracontrolled dis- tribution, which is defined by global but nonlocal op- erators. Our aim is to find an equivalence between these two notions..
4. 星野壮登, A relation between modeled distributions and paracontrolled distributions, The AIMS Conference Series on Dynamical Systems and Differential Equations, 2018.07, In the world of singular SPDEs, there are two big theories: the theory of regularity structures by Hairer and the paracontrolled calculus by Gubinelli, Imkeller and Perkowski. In Hairer’s theory, the solu- tion is defined as a modeled distribution, which rep- resents a local behavior of the solution. In the GIP theory, the solution is defined as a paracontrolled dis- tribution, which is defined by global but nonlocal op- erators. Our aim is to find an equivalence between these two notions..
5. @星野壮登, A relation between modeled distributions and paracontrolled distribitions, 確率論シンポジウム, 2017.12.
6. @星野壮登, Global well-posedness of comples Ginzburg-Landau equation with a space-time white noise, Stochastic Analysis on Large Scale Interacting Systems, 2017.11.
7. @星野壮登, (1) Global well-posedness of complex Ginzburg-Landau equation with a space-time white noise, (2) A coupled KPZ equation, its two types of approximations and existence of global solutions, 日本数学会2017年度秋季総合分科会, 2017.09.
8. @星野壮登, Global solution of the coupled KPZ equations, 確率論シンポジウム, 2016.12.
9. @星野壮登, (1) Hairer理論の$¥Phi^4$モデルへのアプローチの概説, (2) Global well-posedness of singular stochastic PDEs, 確率解析とその周辺, 2016.11.
10. @星野壮登, Paracontrolled calculus and Funaki-Quastel approximation for KPZ equation, 確率論シンポジウム, 2015.12.
11. @星野壮登, KPZ equation with fractional derivatives of white noise, 確率解析とその周辺, 2015.10.
学会活動
所属学会名
日本数学会
学術論文等の審査
年度 外国語雑誌査読論文数 日本語雑誌査読論文数 国際会議録査読論文数 国内会議録査読論文数 合計
2019年度      
2018年度      
2016年度      
2015年度      
受賞
東京大学総長賞, 東京大学, 2016.03.
日本数学会賞建部賢弘奨励賞, 日本数学会, 2017.09.
研究資金
科学研究費補助金の採択状況(文部科学省、日本学術振興会)
2019年度~2022年度, 若手研究, 代表, 繰り込みを伴う非線形確率偏微分方程式の解析に対する一般理論.
2016年度~2017年度, 特別研究員奨励費, 代表, 特異な確率偏微分方程式に対する近似理論の正則性構造理論による研究.

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