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.

Updated version as published

References in corpus (5)

• Universal Record Statistics of Random Walks and Lévy Flights
• Record statistics for biased random walks, with an application to financial data
• Record statistics and persistence for a random walk with a drift
• Universal statistics of longest lasting records of random walks and Lévy flights
• Anomalous diffusions induced by enhancement of memory

Cited by in corpus (5)

• Record statistics for random walks and Lévy flights with resetting
• Statistics of the Number of Records for Random Walks and Lévy Flights on a $1D$ Lattice
• 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