標(biāo)題：Singular kinetic McKean-Vlasov SDEs
報(bào)告時(shí)間：2024年11月4日（星期一）15：30-16：30
報(bào)告地點(diǎn)：線(xiàn)上騰訊會(huì)議（會(huì)議ID：513-157-445）
主講人：郝子墨
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告內(nèi)容簡(jiǎn)介：
In this talk, we delve into mean-field kinetic stochastic differential equations (SDEs) featuring Gaussian environment noise and singular interaction kernels driven by Brownian motion and α-stable processes. First, we develop paracontrolled calculus within the kinetic framework when the driving noise is Brownian motion. Applying this, we establish global well-posedness for nonlinear singular kinetic equations with both singular environment noise and bounded interaction kernel, contingent upon the well-definition of the products of singular terms. We obtain how such products can be defined in scenarios where the singular term is a Gaussian random field. Second, when the driving noise takes an α-stable process, we give the well-posedness and provide quantitative estimates for the propagation of chaos related to the kinetic SDEs endowed with singular interaction kernels, such as the Coulomb potential, and devoid of environment noise (The talk is based on joint works with Jean-Francois Jabir, Stephane Menozzi, Michael R¨ockner, Xicheng Zhang, Rongchan Zhu and Xiangchan Zhu).
主講人簡(jiǎn)介：
郝子墨于2023年博士畢業(yè)于武漢大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院和Bielefeld大學(xué)數(shù)學(xué)學(xué)院?，F(xiàn)為Bielefeld大學(xué)博士后研究員。主要研究方向?yàn)槠娈愊禂?shù)的SDE。已在 J. Math. Pures Appl., SIAM J. Math. Anal., Bernoulli等國(guó)際權(quán)威期刊發(fā)表多篇學(xué)術(shù)論文。
