渐近鞅的局部收敛性

渐近鞅的局部收敛性 LOCAL CONVERGENCE OF AMARTS 甘师信 Gan Shixin 1 first-author Department of Mathematics Wuhan University Wuhan Hubei Department of Mathematics Wuhan University Wuhan Hubei Department of Mathematics, Wuhan University Department of Mathematics, Wuhan University 1953年,J.L.Doob讨论了鞅的局部收敛性,后来,Y.S.Chow,H.J.Engelbert等人进一步讨论了鞅及下鞅的局部收敛性,得到了很多重要结果,渐近鞅（Amart）是鞅的重要推广,而且,它保持了鞅的一些最基本性质,如极值不等式、可选停时定理、可选采样定理、Riesz分解等,然而对渐近鞅的局部收敛性很少有文献论及。本文的目的是对渐近鞅的局部收敛性作些探讨,得到了渐近鞅局部收敛性的若干结果,它们是鞅的有关结论的推广与改进,同时还证明了极限鞅（X n ）在积分渐近一致绝对连续的条件下,lim X n a.s.存在且有限。由于实值情形渐近鞅一定是极限鞅,因此这个结论对渐近鞅自然成立。 1953, Doob investigated local Convergence of martingales. Afterwards, Y.S. Chow, H.J.Engelbert and some others further discussed local convergence of martingales and Submartingales. They obtained many important results. Arnarts are important extensions of martingales and they reserve Some basic properties of martingales. But local Convergence of amarts is seldom tou-ched The purpose of this paper is to discuss local Convergence of amarts. Some results of local Convergence of amarts are obtained. 鞅 渐近鞅 极限鞅 局部收敛性 Riesz分解 积分渐近一致绝对连续 martingale Amart martingale in the limit local Convergence Riesz decomposition asymptotically uniform Continuity of integrals. 高等学校科学技术基金 1988-02-01 2021-04-01 2