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

TL;DR

This paper analyzes record statistics in a correlated discrete-time random walk, revealing how long-term memory and correlations influence record events and differ from independent step models.

Contribution

It provides exact calculations of record-related quantities for a correlated random walk, highlighting novel behaviors due to strong correlations.

Findings

Correlations induce super-diffusivity and transience.

Record statistics differ significantly from independent step walks.

Exact formulas for record-related quantities are derived.

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.