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Asymptotic analysis of the elephant random walk
Journal of Statistical Mechanics: Theory and Experiment ( IF 2.2 ) Pub Date : 2021-01-07 , DOI: 10.1088/1742-5468/abcd36 Cristian F Coletti , Ioannis Papageorgiou
Journal of Statistical Mechanics: Theory and Experiment ( IF 2.2 ) Pub Date : 2021-01-07 , DOI: 10.1088/1742-5468/abcd36 Cristian F Coletti , Ioannis Papageorgiou
In this work we study asymptotic properties of a long range memory random walk known as elephant random walk. Using Lyapunov functions we prove recurrence and transience for the elephant random walk. Finally, in the recurrent regime, we establish the replica mean field limit for this random walk.
中文翻译:
大象随机游走的渐近分析
在这项工作中,我们研究了称为大象随机游走的长程记忆随机游走的渐近特性。使用李雅普诺夫函数,我们证明了大象随机游走的递归性和瞬时性。最后,在循环机制中,我们为这个随机游走建立了副本平均场限制。
更新日期:2021-01-07
中文翻译:
大象随机游走的渐近分析
在这项工作中,我们研究了称为大象随机游走的长程记忆随机游走的渐近特性。使用李雅普诺夫函数,我们证明了大象随机游走的递归性和瞬时性。最后,在循环机制中,我们为这个随机游走建立了副本平均场限制。