论文标题
限制定理以随机步行，并通过动态系统扰动内存
Limit theorems for a random walk with memory perturbed by a dynamical system
论文作者
论文摘要
我们引入了一个新的随机步行，并以无限的记忆作为大象随机行走的混合物和动态随机步行的混合物获得，我们称之为动态大象随机步行（DERW）。由于这种混合物的结果，所得随机过程的增量分布取决于时间。我们证明了DERW的强大定律，在特定情况下，我们为其速度提供了明确的表达方式。最后，我们为中心限制定理和迭代对数定律提供了足够的条件。
We introduce a new random walk with unbounded memory obtained as a mixture of the Elephant Random Walk and the Dynamic Random Walk which we call the Dynamic Elephant Random Walk (DERW). As a consequence of this mixture the distribution of the increments of the resulting random process is time dependent. We prove a strong law of large numbers for the DERW and, in a particular case, we provide an explicit expression for its speed. Finally, we give sufficient conditions for the central limit theorem and the law of the iterated logarithm to hold.
