Even simply defined, finite-state generators produce stochastic processes that require
tracking an uncountable infinity of probabilistic features for optimal prediction. For processes …

Renewal processes are broadly used to model stochastic behavior consisting of isolated
events separated by periods of quiescence, whose durations are specified by a given …

We present two examples of finite-alphabet, infinite excess entropy processes generated by
stationary hidden Markov models (HMMs) with countable state sets. The first, simpler …

Identifying and quantifying memory are often critical steps in developing a mechanistic
understanding of stochastic processes. These are particularly challenging and necessary …

Recurrent neural networks are used to forecast time series in finance, climate, language,
and from many other domains. Reservoir computers are a particularly easily trainable form …

We introduce a simple analysis of the structural complexity of infinite-memory processes
built from random samples of stationary, ergodic finite-memory component processes. Such …

Recurrent neural networks are used to forecast time series in finance, climate, language,
and from many other domains. Reservoir computers are a particularly easily trainable form …

The article discusses two mutually-incompatible hypotheses about the stochastic
mechanism of the generation of texts in natural language, which could be related to entropy …

The relaxed Hilberg conjecture states that the mutual information between two adjacent
blocks of text in natural language grows as a power of the block length. The present paper …

We supply corrected proofs of the invariance of completion and the chain rule for the
Shannon information measures of arbitrary fields, as stated by Dębowski in 2009. Our …