We consider the extreme value statistics of centrally-biased random walks with asymptotically-zero drift in the ergodic regime. We fully characterize the asymptotic distribution of the maximum for this class of Markov chains lacking translational invariance, with a particular emphasis on the relation between the time scaling of the expected value of the maximum and the stationary distribution of the process.
Artuso, R., Onofri, M., Pozzoli, G., Radice, M. (2022). Extreme value statistics of positive recurrent centrally biased random walks. JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT, 2022(10) [10.1088/1742-5468/ac98bd].
Extreme value statistics of positive recurrent centrally biased random walks
Pozzoli, G;
2022
Abstract
We consider the extreme value statistics of centrally-biased random walks with asymptotically-zero drift in the ergodic regime. We fully characterize the asymptotic distribution of the maximum for this class of Markov chains lacking translational invariance, with a particular emphasis on the relation between the time scaling of the expected value of the maximum and the stationary distribution of the process.
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