主講人：黃乘明 華中科技大學(xué)教授

時(shí)間：2022年12月7日10：00

地點(diǎn)：騰訊會(huì)議 145 497 173

舉辦單位：數(shù)理學(xué)院

主講人介紹：黃乘明，華中科技大學(xué)教授、博士生導(dǎo)師；兼任中國(guó)數(shù)學(xué)會(huì)計(jì)算數(shù)學(xué)分會(huì)常務(wù)理事；曾經(jīng)和現(xiàn)任J Comput Appl Math、J Frankl Inst等4個(gè)SCI期刊編委。主要從事微分方程數(shù)值計(jì)算研究，主持國(guó)家自然科學(xué)基金項(xiàng)目7項(xiàng)，在SINUM、SISC、Numer Math、IMAJNA、JCP、JSC等學(xué)術(shù)期刊發(fā)表SCI論文100余篇。

內(nèi)容介紹：In this talk we first establish the existence, uniqueness and H?lder continuity of the solution to stochastic Volterra integral equations (SVIEs) with weakly singular kernels, with singularities α ∈ (0, 1) for the drift term and β ∈ (0, 1/2) for the stochastic term. Subsequently, we propose a θ-Euler–Maruyama scheme and a Milstein scheme to solve the equations numerically and obtain strong rates of convergence for both schemes in Lp norm for any p ≥1. For the θ-Euler–Maruyama scheme the rate is min{1?α, 1/2?β} and for the Milstein scheme is min{1?α, 1?2β}. These results on the rates of convergence are significantly different from those it is similar schemes for the SVIEs with regular kernels. This talk is based on the joint work with Dr. Min Li and Professor Yaozhong Hu.