数学物理学报(英文版) ›› 1987, Vol. 7 ›› Issue (1): 43-55.

• 论文 • 上一篇    下一篇

CONTINUOUS-TIME STOCHASTIC APPROXIMATION PROCEDURE WITH RANDOMLY VARYING TRUNCATIONS

陈翰馥1, 吴春涛2, 朱允民2   

  1. 1. Institute of Systems Science, Academia Sinica, Beijing, China;
    2. Institute of Mathematical Sciences, Chengdu Branch, Academia Sinica, Chengdu, China
  • 收稿日期:1984-11-14 出版日期:1987-03-25 发布日期:1987-03-25

CONTINUOUS-TIME STOCHASTIC APPROXIMATION PROCEDURE WITH RANDOMLY VARYING TRUNCATIONS

Chen Hanfu1, Wu Chuntao2, Zhu Yunmin2   

  1. 1. Institute of Systems Science, Academia Sinica, Beijing, China;
    2. Institute of Mathematical Sciences, Chengdu Branch, Academia Sinica, Chengdu, China
  • Received:1984-11-14 Online:1987-03-25 Published:1987-03-25

摘要: In this paper a continuous-time stochastic approximation (S.A.) procedure with randomly varying truncations is proposed, and for its convergence to the value to be sought for it is proved that the conditions imposed on the regression function are rather weak and neither the independence of the increment of the error process nor the boundedness of the procedure are required. The convergence rate and the asymptotic properties for a class of measurement errors are also concerned.

Abstract: In this paper a continuous-time stochastic approximation (S.A.) procedure with randomly varying truncations is proposed, and for its convergence to the value to be sought for it is proved that the conditions imposed on the regression function are rather weak and neither the independence of the increment of the error process nor the boundedness of the procedure are required. The convergence rate and the asymptotic properties for a class of measurement errors are also concerned.