Weak Convergence of Hilbert-valued Semimartingale Sequence

The convergence of Hilbert-valued semimartingales to continuous semimartingales are discussed under the condition UT. And the stability of stochatic differential equations of type X^n=\int_0 a^n\left(X^n, s\right) d Y_s^n+\int_0 b^n\left(X^n, s\right) d A_s^n, \quad X_0^n=0 \quad \forall n \geq 1 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.