Related papers: On the Entropy Rate of Pattern Processes
This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching…
The paper analyses stochastic systems describing reacting molecular systems with a combination of two types of state spaces, a finite-dimensional, and an infinite dimenional part. As a typical situation consider the interaction of larger…
A regular Hilberg process is a stationary process that satisfies both a hyperlogarithmic growth of maximal repetition and a power-law growth of topological entropy, which are a kind of dual conditions. The hyperlogarithmic growth of maximal…
Semi-Markov processes play an important role in the effective description of partially accessible systems in stochastic thermodynamics. They occur, for instance, in coarse-graining procedures such as state lumping and when analyzing waiting…
In this document, we introduce a notion of entropy for stochastic processes on marked rooted graphs. For this, we employ the framework of local weak limit theory for sparse marked graphs, also known as the objective method, due to…
The complexity function of an infinite word $w$ on a finite alphabet $A$ is the sequence counting, for each non-negative $n$, the number of words of length $n$ on the alphabet $A$ that are factors of the infinite word $w$. For any given…
Extropy, a complementary dual of entropy, (proposed by Lad et al. \cite{lad2015extropy} in 2015) has attracted considerable interest from the research community. In this study, we focus on discrete random variables and define conditional…
Given a growth rule which sequentially constructs random permutations of increasing degree, the stochastic process version of the rencontre problem asks what is the limiting proportion of time that the permutation has no fixed points…
This work derives a theoretical value for the entropy of a Linear Additive Markov Process (LAMP), an expressive model able to generate sequences with a given autocorrelation structure. While a first-order Markov Chain model generates new…
Maximal repetition of a string is the maximal length of a repeated substring. This paper investigates maximal repetition of strings drawn from stochastic processes. Strengthening previous results, two new bounds for the almost sure growth…
The selection of an equilibrium state by maximising the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of…
We study the statistics of infima, stopping times and passage probabilities of entropy production in nonequilibrium steady states, and show that they are universal. We consider two examples of stopping times: first-passage times of entropy…
The Poisson process is the most elementary continuous-time stochastic process that models a stream of repeating events. It is uniquely characterised by a single parameter called the rate. Instead of a single value for this rate, we here…
We show that under local detailed balance the expected entropy production rate is always bounded in terms of the dynamical activity. The activity refers to the time-symmetric contribution in the action functional for path-space…
For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…
Near equilibrium, thermodynamic intuition suggests that fast, irreversible processes will dissipate more energy and entropy than slow, quasistatic processes connecting the same initial and final states. Here, we test the hypothesis that…
We consider the asymptotic behavior of the expectation of the maximum for a special assignment process with constant or i.i.d. coefficients. We show how it depends on the coefficients' distribution.
We introduce a class of stochastic integer sequences. In these sequences, every element is a sum of two previous elements, at least one of which is chosen randomly. The interplay between randomness and memory underlying these sequences…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
Order patterns apply well to many fields, because of minimal stationarity assumptions. Here we fix the methodology of patterns of length 3 by introducing an orthogonal system of four pattern contrasts. These contrasts are statistically…