B值随机变量序列的变换与局部强大数定律

B值随机变量序列的变换与局部强大数定律 TRANSFORMS FOR BANACH SPACE VALUED RANDOM VARIABLE SEQUENCES AND LOCAL STRONG LAW OF LARGE NUMBERS 甘师信 Gan Shixin 1 2 first-author 武汉大学数学系,武汉 武汉大学数学系,武汉 Department of mathematics, Wuhan University Department of mathematics, Wuhan University ,430072 ,430072 本文讨论了一般B值可积适应序列的变换及其收敛性,得到了变换的局部收敛性及局部强大数律。同时用变换的局部收敛性刻划了B空间的光滑性。 In this paper we discuss the transforms for general Banach space valued random variable sequences and their convergence. We obtain some general results concerning local convergence and local strong law of large numbers of such transforms. In the other direction, p-smoothness of Banach spaces are characterized in terms of local convergence of such transforms. 阶可光滑空间 B值可积适应序列的变换 局部收敛性 局部强大数律 p-smoothable space transform of Banach space valued integrable adapted sequence local Convergence local strong law of large numbers O211.4 博士学科点专项基金;国家自然科学基金(61672102) 1993-03-01 2021-04-01 3