Record Ages of Scale Invariant non-Markovian Random Walks
arXiv:2305.09642 · doi:10.1038/s41467-023-41945-9
Abstract
How long is needed for an observable to exceed its previous highest value and establish a new record? This time, known as the age of a record plays a crucial role in quantifying record statistics. Until now, general methods for determining record age statistics have been limited to observations of either independent random variables or successive positions of a Markovian (memoryless) random walk. Here we develop a theoretical framework to determine record age statistics in the presence of memory effects for continuous non-smooth processes that are asymptotically scale-invariant. Our theoretical predictions are confirmed by numerical simulations and experimental realizations of diverse representative non-Markovian random walk models and real time series with memory effects, in fields as diverse as genomics, climatology, hydrology, geology and computer science. Our results reveal the crucial role of the number of records already achieved in time series and change our view on analysing record statistics.
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Cited by in corpus (7)
- Record Ages of Scale Invariant non-Markovian Random Walks
- Optimal conditions for first passage of jump processes with resetting
- Persistent and anti-Persistent Motion in Bounded and Unbounded Space: Resolution of the First-Passage Problem
- From Maximum of Intervisit Times to Starving Random Walks
- Full Record Statistics of 1d Random Walks
- On Approximate Representation of Fractional Brownian Motion
- Anomalous Diffusion and Emergent Universality in Coupled Memory-Driven Systems