【摘要】 本文在无穷维Hilbert空间中研究了一类具有马尔可夫调制的随机微分方程(SDEwMSs).在一般情况下SDEwMSs没有解析解.因此合适的数值逼近法,例如欧拉法,就是在研究它们性质时所采用的重要工具.本文在较弱的条件下不仅证明了欧拉近似解收敛于SDEwMSs的精确解(分析解),而且给出了欧拉近似阶的界.更多还原

【Abstract】 This paper studies a class of stochastic di ff erent equations with Markovian switching (SDEwMSs) in the infinite dimensional H ilbert space.In general SDEwMSs do not have explicit solutions.Appropriate numer ical approximations,such as the Euler scheme,are therefore a vital tool in explo ring their porperties.In this paper,it is proved that the Euler approximate solu tions will converge to the exact solutions for SDEwMSs under weaker conditions.T he bound to the order of the Euler approximation is also provided.更多还原