Record statistics for a discrete-time random walk with correlated steps

Abstract

The characterization of record events is considered for a discrete-time random walk model with long-term memory arising from correlations between successive steps. An important feature is that the correlations are strong enough to give rise to super-diffusivity and transience. Various quantities related to record statistics are calculated exactly, highlighting important differences in behaviour from the simple random walk with independent steps.

arXiv commentUpdated version as published

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• Record statistics for random walks and Lévy flights with resetting
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• Universal survival probability for a correlated random walk and applications to records
• Record Ages of Scale Invariant non-Markovian Random Walks
• Exact and asymptotic properties of $\delta$-records in the linear drift model