標(biāo)題：Near-Optimality in Two-Time-Scale Stochastic Optimal Control Systems with Infinite Integral-type Delays
報(bào)告時(shí)間：2025年11月13日（星期四）13:30-14:30
報(bào)告地點(diǎn)：線(xiàn)上騰訊會(huì)議（會(huì)議ID：257423694）
主講人：吳付科
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：
This paper focuses on near-optimal controls for a class of fully-coupled, two-time-scale stochastic functional differential equations (SFDEs). The coefficients of the system involve infinite integral-type delays in both the slow and fast components, which induces a loss of the Markov property. To overcome this challenge, the original system is first transformed into a higher-dimensional system without delay via state augmentation. The core of the analysis is an averaging principle. To ensure its successful application, the ergodicity of the resulting high-dimensional fixed-X equation and its continuous dependence on parameters are established. A key result is the convergence of the value function of the original system to that of a simplified, limiting system, whose coefficients are averages with respect to the invariant measure of the fixed-X equation. Finally, a two-time-scale optimal control problem for an advertising model is presented as an illustrative example.
主講人簡(jiǎn)介：
吳付科，華中科技大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院教授，博士生導(dǎo)師，國(guó)家級(jí)高層次青年人才，入選教育部新世紀(jì)優(yōu)秀人才支持計(jì)劃。主持國(guó)家自然科學(xué)基金委重點(diǎn)項(xiàng)目、面上項(xiàng)目、教育部新世紀(jì)優(yōu)秀人才基金、英國(guó)皇家學(xué)會(huì)“高級(jí)牛頓學(xué)者”基金和美國(guó)數(shù)學(xué)學(xué)會(huì)（AMS）訪(fǎng)問(wèn)基金等。主要從事隨機(jī)微分方程以及相關(guān)領(lǐng)域的研究。近年來(lái)，在SIAM系列雜志, JDE,SPA等期刊發(fā)表論文100余篇。出版一部專(zhuān)著《隨機(jī)微分方程》和1部譯著《隨機(jī)微分方程：導(dǎo)論與應(yīng)用》，當(dāng)前為《IET Control Theory & Applications》編委。
