Mil的另一收敛定理及某些鞅型序列的稳定性  

ANOTHER CONVERGENCE THEOREM OF MIL AND STABILITY PROPERTIES OF SOME MARTINGALE-LIKE SEQUENCES

作　　者：甘师信[1] 

机构地区：[1]武汉大学

出　　处：《数学杂志》1989年第3期327-336,共10页Journal of Mathematics

基　　金：国家教委基金的课题

摘　　要：本文证明了(1)设(X_n,■_n)为M.Talagrand意义下的mil且满足条件C^+:τ∈T,其中T为(■_n)停时全体构成的集合,则(X_n)a.s.收敛.(2)设(X_n,■_n)为渐近一致可积的适应序列,则(X_n)a.s.收敛与(X_n)为mil等价.(3)L^1极限鞅,GFT(game fairer with time)及M.Talagrand意义下的mil在函数f:R→R满足条件:①连续②当|x|→∞,f(x)=O(x)时具有稳定性.In this paper we prove that (1) if (X_n,) is a mil in M. Talagrand′s sense which satisfies the assumption where T is the set of all stopping times with respect to(), then(X_n) converges almost surely. (2) Assume(X_n, )is an assymptotically uniformly integrable adapted sequence, then the following are equivalent:(a)(X_n) converges almost surely,(b) (X_n) is a mil, (3) A sufficient condition is given for stability of martingale in L^1-limit, GFT and mil in M. Talagrand's sense.

关 键 词：随机变数列 鞅型序型 收敛定理 

分 类 号：O211.4[理学—概率论与数理统计]