Kyushu University Academic Staff Educational and Research Activities Database
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Masato Hoshino Last modified date:2020.01.31

Academic Degree
Ph. D. (Mathematical Sciences)
Country of degree conferring institution (Overseas)
Field of Specialization
Probability Theory
Total Priod of education and research career in the foreign country
Research Interests
  • Singular SPDEs
    keyword : rough path theory, regularity structures, paracontrolled calculus
Academic Activities
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.
1. 星野 壮登, Paracontrolled calculus and regularity structures, 確率解析とその周辺, 2019.11.
2. 星野 壮登, Paracontrolled Calculus and Regularity Structures, The 12th Mathematical Society of Japan, Seasonal Institute, 2019.07.
3. 星野 壮登, A relation between modelled distributions and paracontrolled distributions, Equadiff 2019, 2019.07, I will discuss the relation between the theory of regularity structures and the paracontrolled calculus. First I will show the equivalence of admissible models and their paracontrolled representations. Second I will explain a strategy to prove the equivalence of modelled distributions and paracontrolled distributions. This talk is based on a joint work with Ismael Bailleul..
4. 星野 壮登, Coupled KPZ equations, 2019 IMS-China International Conference on Statistics and Probability, 2019.07, First, we explain the research with T. Funaki on the local well-posedness of the coupled KPZ equations. We show the global well-posedness under the so-called "trilinear" condition. If there is time, we also explain the recent research with I. Bailleul on the regularity structures and paracontrolled calculus. This research will be useful to consider more general KPZ equations..
5. 星野壮登, A relation between regularity structures and paracontrolled calculus, Stochastic Analysis on Large Scale Interacting Systems, 2018.11.
6. 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..
7. @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.
8. @星野壮登, KPZ equation with fractional derivatives of white noise, 確率解析とその周辺, 2015.10.
Membership in Academic Society
  • Mathematical Society of Japan