论文标题
使用Martingale方法对增强大象随机步行的新见解
New insights on the reinforced Elephant Random Walk using a martingale approach
论文作者
论文摘要
本文致力于使用Martingale方法对增强大象随机行走（RERW）的渐近分析。在扩散和关键的制度中，我们建立了几乎确定的融合，迭代对数定律以及二次互惠的强大法则。还提供了RERW与某些高斯过程的分布收敛。在超级未来的制度中，我们证明了分布收敛以及RERW的平方融合。我们所有的分析都依赖于具有矩阵归一化的多维Martingales的渐近结果。
This paper is devoted to the asymptotic analysis of the reinforced elephant random walk (RERW) using a martingale approach. In the diffusive and critical regimes, we establish the almost sure convergence, the law of iterated logarithm and the quadratic strong law for the RERW. The distributional convergences of the RERW to some Gaussian processes are also provided. In the superdiffusive regime, we prove the distributional convergence as well as the mean square convergence of the RERW. All our analysis relies on asymptotic results for multi-dimensional martingales with matrix normalization.
