Weak convergence of Hilbert-valued semimartingale sequence

Abstract

The convergence of Hilbert-valued semimartingales to continuous semimartingales are discussed under the condition UT. And the stability of stochatic differential equations of type is discussed under jointly weak convergence of driving processes {(Yn, An)}n≥1, where Yn and An are H-valued semimartingale and H-valued finite variation with every component being increasing process, respectively. 本文在条件 ＵＴ下研究了 Ｈｉｌｂｅｒｔ－值半鞅序列到连续 Ｈｉｌｂｅｒｔ－值半鞅的收敛性，并在弱收敛的条件下研究了形如 Ｘｎ＝ ａｎ（Ｘｎ，ｓ）ｄＹｎｓ＋ ｂｎ（Ｘｎ，ｓ）ｄＡｎｓ， Ｘｎｏ＝ ０ ｎ≥１随机微分方程的稳定性，其中Ｙｎ和Ａｎ分别为Ｈｉｌｂｅｒｔ－值半鞅和分量为增过程的Ｈｉｌｂｅｒｔ－值有限变差过程．