Hilbert-值半鞅序列的弱收敛

Weak Convergence of Hilbert-valued Semimartingale Sequence

  • 摘要: 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 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 随机微分方程的稳定性,其中YnAn分别为Hilbert-值半鞅和分量为增过程的Hilbert-值有限变差过程。

     

    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 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, Ann≥1, where Yn and An are H-valued semimartingale and H-valued finite variation with every component being increasing process, respectively.

     

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