应兰州大学数学与统计学院邀请，加拿大Alberta大学胡耀忠教授将于2026年7月31日-8月8日访问兰州大学，并于2026年8月1日-8月3日进行学术报告，欢迎全校师生参加。

报告I 题目:Matching upper and lower moment bounds for alarge class of stochastic PDEs driven by generalspace-time Gaussian noises

报告摘要：Inthistalk, I will presentmatching upper and lower moment bounds for the solutionto stochastic partial differential equationdriven by a general Gaussian noise, giving acomplete answer to the open problem of the matching lower moment bounds for thestochastic wave equations driven by a general Gaussian noise. Two new conditionsare introduced for theGreen'sfunction of the equation to assure this intermittencyproperty:smallballnondegeneracyandbounded Hardy-Littlewood-Sobolev totalmass, which are satisfied by a large class of stochastic PDEs, including stochasticheat equations, stochastic wave equations,stochastic heat equationswith fractionalLaplacians,and stochastic partial differential equations with fractional derivativesboth in time and in space. The main technique to obtain the lower moment bounds isto develop a Feynman diagram formula for the moments of the solution, to find themanageable main terms, and to carefully analyse these terms of sophisticated multipleintegrals by exploring the above two properties. This is a joint work with Xiong Wang.

时 间：2026年8月1日（星期六）下午16：00.

地 点：理工楼631

报告II 题目:Feynman-Kac formula for general time dependent stochastic parabolic equation on a bounded domain and applications

报告摘要：In this talk,I will present a joint work with Qun Shi on Feynman-Kacformulato representthe solutionto generaltime inhomogeneous stochastic parabolic partial differential equations driven bymultiplicative fractional Gaussian noisesinbounded domain:$\frac{\partialu(t,x)}{\partialt}=L_tu(t,x)+u(t,x)\dot{W}(t,x)$, where $L_t$ is a second order uniformly ellipticoperator whose coefficients can depend on time and generates a time inhomoegenous Markov process. Theidea is to usetheAronson bounds of fundamental solution of the associated heatkernel andthe techniques from Malliavin calculus.The newly obtainedFeynman-Kacformula is then applied to establish the H\"older regularity inthe spaceand time variables.Thedependenceon time of the coefficientsposesserious challenges and new results about the stochastic differential equations are discovered to face the challenge. An amazing application of the Feynman-Kac formula is about the matching upper andlower bounds for all moments of the solution,an critical tool for the intermittency. For the latter result we need first to establishnew small ball like boundsfor the diffusion associated with the parabolic differential operatorin the bounded domain which is of interest on its own.

时 间：2026年8月2日（星期日）下午16：00.

地 点：理工楼631

报告III 题目:Stochastic wave equation with additive fractional noise: Solvability and global H\"oldercontinuity

报告摘要：In this talk, I will present joint work with Shuhui Liu and Xiong Wang about the necessary and sufficient conditions to solvestochastic wave equation $\frac{\partial^2 }{\partial t^2}u(t,x) =\Delta u(t,x)+\dot{W}(t,x)$ in $L^2$, where $\{W(t,x),t\ge 0,x\in \mathbb{R}^d\} $ is a fractional Brownian field with temporal Hurst parameter $H_0\ge1/2$ and spatial Hurst parameters $H_i\in(0,1)$ for $i=1,\cdots,d$. I will also discuss the sharp growth rate and the sharp H\"older continuity of the solution on the whole space $\mathbb{R}^d$ when$d=1$and $H_0=1/2$. The idea for the latter result is to use Talagrand's theorem whichrequiresprecise upper and lower bounds for the correspondingnatural metricdenotedas$d_1((t,x),(s,y))=\sqrt{\mathbb{E}|u(t,x)-u(s,y)|^2}$associated with the solution$u(t,x)$.

时 间：2026年8月3日（星期一）下午16：00.

地 点：理工楼631

欢迎广大师生光临!

报告人简介

胡耀忠教授(Yaozhong Hu)自1982年大学毕业后，在李国平院士的指导下，开始从事系统科学、随机力学等领域的研究;并于1984年从中国科学院武汉数学物理研究所硕士毕业后，留在该研究所工作。他先后于1986底-1988初和1991年初-1992年初两次派往法国，师从国际上著名概率学家P.A.Meyer从事随机分析研究，并于1992年初在法国取得博士学位;先后在法国斯特拉斯堡大学，挪威奥斯陆大学，德国波鸿鲁尔大学，美国的北卡罗来纳大学教堂山分校，美国的加州大学尔湾分校工作学习。 于1997年至2017年在美国Kansas大学任助理教授、副教授、教授;2017年8月起到加拿大Alberta大学任Centennial Professor。胡教授长期从事概率统计、随机系统的理论及其在金融、工程、量子物理中的应用研究，在概率统计领域的一流期刊等发表论文近200多篇;2015年当选美国统计研究院会士(Fellow of Instituteof MathematicalStatistics).

甘肃省计算数学基础学科研究中心

数学与统计学院

萃英学院

2026年7月27日