次线性期望下m-AANA序列线性过程的强大数定律

Strong Law of Large Numbers for Linear Processes of m-AANA Sequences under Sublinear Expectations

摘要

在次线性期望框架下,对于以m-渐近几乎负相依(m-AANA)随机变量序列作为创新项构造的线性过程,结合次线性期望空间中的概率不等式、Toeplitz定理与Borel-Cantelli引理,在线性过程的系数列绝对可求和与创新项满足一致矩条件的假设下,给出该线性过程的强大数定律.

Abstract

Within the framework of sublinear expectations,for linear processes constructed by m-asymptotically almost negatively associated (m-AANA) random variable sequences as innovations,combined with probabilistic inequalities in sublinear expectation space,the Toeplitz theorem and the Borel-Cantelli lemma,and under the assumptions that the coefficient sequence of the linear process is absolutely summable and that the innovations satisfy a uniform moment condition,we give the strong law of large numbers for this linear process.

关键词

强大数定律 / m-AANA随机变量序列 / 线性过程 / 次线性期望

Key words

strong law of large numbers / m-AANA random variable sequence / linear process / sublinear expectation

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基金资助

国家自然科学基金(12001256)