Chinese Quarterly Journal of Mathematics ›› 2009, Vol. 24 ›› Issue (1): 35-39.

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A Convergence Theorem for Set-valued Eventual Supermartingle 

  

  1. Department of Mathematics, Engineering College of Armed Police Force
  • Received:2005-04-01 Online:2009-03-30 Published:2023-09-06
  • About author: LI Gao-ming(1961- ), male, native of Fufeng, Shannxi, a professor of Engineering College of Armed Policed Force, M.S.D., engages in set-valued stochastic process and set-valued analysis.

Abstract: In this paper, the properties of set-valued Eventual Supermartingle are discussed. The main result is that suppose {Fn,n ≥ 1}   be set-valued Eventual Supermartingle, if supTE(d(0,Fτ)) < ∞, then Fn →F and SF1= Φ, here T is the sets of all bounded stopping times.

Key words: set-valued Eventual Martingale, Kuratowski convergence

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