主講人：楊洪福  廣西師范大學(xué)教師

時(shí)間：2021年11月5日14：00

地點(diǎn)：騰訊會(huì)議 516 157 788

舉辦單位：數(shù)理學(xué)院

主講人介紹：楊洪福，博士，2019年畢業(yè)于東北師范大學(xué)，國(guó)防科技大學(xué)博士后，廣西師范大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院教師。主要從事隨機(jī)微分方程穩(wěn)定性理論、應(yīng)用及數(shù)值逼近的研究，在此研究方向上發(fā)表了學(xué)術(shù)論文近10篇，部分研究成果已發(fā)表在SIAM  J. Numer. Anal.、Math. Comp.、J. Differential Equations、Internat. J.  Control、Discrete Cont. Dyn.  Sys.-B、數(shù)學(xué)年刊A輯等；出版學(xué)術(shù)專(zhuān)著和研究生教材各1部；主持國(guó)家自然科學(xué)基金青年基金、廣西省自然科學(xué)基金青年基金、廣西科技計(jì)劃人才專(zhuān)項(xiàng)項(xiàng)目各1項(xiàng)；參加國(guó)家自然科學(xué)基金面上項(xiàng)目1項(xiàng)。

內(nèi)容介紹：In this article we introduce a number of explicit schemes, which are amenable to  Khasminski's technique and are particularly suitable for highly nonlinear  stochastic differential equations (SDEs). We show that without additional  restrictions to those which guarantee the exact solutions possess their  boundedness in expectation with respect to certain Lyapunov-type functions, the  numerical solutions converge strongly to the exact solutions in finite-time.  Moreover, based on the convergence theorem of nonnegative semimartingales,  positive results about the ability of the explicit numerical scheme proposed to  reproduce the well-known LaSalle-type theorem of SDEs are proved here, from  which we deduce the asymptotic stability of numerical solutions. Some examples  are discussed to demonstrate the validity of the new numerical schemes and  computer simulations are performed to support the theoretical results. This is a  joint work with Professors Xiaoyue Li and Xuerong Mao.