||星野 壮登, Paracontrolled calculus and regularity structures, 確率解析とその周辺, 2019.11.
||星野 壮登, Paracontrolled Calculus and Regularity Structures, The 12th Mathematical Society of Japan, Seasonal Institute, 2019.07.
||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..
||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..
||星野壮登, A relation between regularity structures and paracontrolled calculus, Stochastic Analysis on Large Scale Interacting Systems, 2018.11.
||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..
||＠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.
||＠星野壮登, KPZ equation with fractional derivatives of white noise, 確率解析とその周辺, 2015.10.