The Asymptotic Behavior of Locally Square Integrable Martingales
The Asymptotic Behavior of Locally Square Integrable Martingales
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DOI：
10.1214/aop/1176988279
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发表时间：
1995-04
影响因子：
2.3
通讯作者：
Jia-gang Wang
中科院分区：
文献类型：
--
作者：
Jia-gang Wang
设M是具有可预测二次方差(M)的局部平方可积鞅，ΔM=M-M-是M的跳跃过程.在对AM的各种约束下，得到了M关于(M)的不同增长率.对于可预测过程B关于M的随机积分X=B.M，A.S.在B的增长率和AM的条件分布或AM的条件矩的约束下，讨论了X的渐近行为将其应用于一些简单的例子，以确定统计量中估计量的收敛速度。
Let M be a locally square integrable martingale with predictable quadratic variance (M) and let ΔM = M - M - be the jump process of M. In this paper, under the various restrictions on AM, the different increasing rates of M in terms of (M) are obtained. For stochastic integrals X = B.M of the predictable process B with respect to M, the a.s. asymptotic behavior of X is also discussed under restrictions on the rates of increase of B and the restrictions on the conditional distributions of AM or on the conditional moments of AM. This is applied to some simple examples to determine the convergence rates of estimators in statistics.