论文标题
将光滑的失忆症引入大象随机步行的记忆
Introducing smooth amnesia to the memory of the Elephant Random Walk
论文作者
论文摘要
本文致力于使用Martingale方法对失忆象随机行走（AERW）进行渐近分析。更确切地说，我们的分析依赖于具有矩阵归一化的多维标准群的渐近结果。在扩散和关键的制度中，我们确定了AERW位置的几乎确定的融合和二次强法。迭代对数定律在关键政权中给出。还提供了AERW与高斯工艺的分布收敛。在超级未来的制度中，我们证明了分布收敛以及AERW的均方根收敛。
This paper is devoted to the asymptotic analysis of the amnesic elephant random walk (AERW) using a martingale approach. More precisely, our analysis relies on asymptotic results for multidimensional martingales with matrix normalization. In the diffusive and critical regimes, we establish the almost sure convergence and the quadratic strong law for the position of the AERW. The law of iterated logarithm is given in the critical regime. The distributional convergences of the AERW to Gaussian processes are also provided. In the superdiffusive regime, we prove the distributional convergence as well as the mean square convergence of the AERW.
