Renewal model for dependent binary sequences

Abstract

We suggest to construct infinite stochastic binary sequences by associating one of the two symbols of the sequence with the renewal times of an underlying renewal process. Focusing on stationary binary sequences corresponding to delayed renewal processes, we investigate correlations and the ability of the model to implement a prescribed autocovariance structure, showing that a large variety of subexponential decay of correlations can be accounted for. In particular, robustness and efficiency of the method are tested by generating binary sequences with polynomial and stretched-exponential decay of correlations. Moreover, to justify the maximum entropy principle for model selection, an asymptotic equipartition property for typical sequences that naturally leads to the Shannon entropy of the waiting time distribution is demonstrated. To support the comparison of the theory with data, a law of large numbers and a central limit theorem are established for the time average of general observables.

References in corpus (8)

• Binary Neural Networks: A Survey
• Inverse statistical problems: from the inverse Ising problem to data science
• Generation of Correlated Binary Sequence from White Noise
• Large Deviations in Discrete-Time Renewal Theory
• Large Deviations in Renewal Models of Statistical Mechanics
• Memory functions and Correlations in Additive Binary Markov Chains
• Iterative Method for Generating Correlated Binary Sequences
• Memory Function versus Binary Correlator in Additive Markov Chains