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In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…
Stochastic thermodynamics extends classical thermodynamics to small systems in contact with one or more heat baths. It can account for the effects of thermal fluctuations and describe systems far from thermodynamic equilibrium. A basic…
The dynamics of the solutions to a class of conservative SPDEs are analysed from two perspectives: Firstly, a probabilistic construction of a corresponding random dynamical system is given for the first time. Secondly, the existence and…
We examine the regenerative cutting process by using a single degree of freedom non-smooth model with a friction component and a time delay term. Instead of the standard Lyapunov exponent calculations, we propose a statistical 0-1 test…
We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include…
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…
We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates $L^n$ of the transfer…
In the first part of the paper the natural scheme for proving noncommutative individual ergodic theorems for multiple sequences is described and applied to obtain results on unrestricted convergence of multiaverages. In the second part…
We study a non Markovian three state model, subjected to an external periodic signal. This model is intended to describe an excitable systems with periodical driving. In the limit of a small amplitude of the external signal we derive…
In this work we introduce and characterize a broad class of quantum operations with a unique fixed point, termed quantum ergodic channels. We derive Lindblad-type master equations for these channels in arbitrary finite dimensions and…
In this paper we present a rigorous analysis of a class of coupled dynamical systems in which two distinct types of components, one excitatory and the other inhibitory, interact with one another. These network models are finite in size but…
Non-equilibrium steady states are subject to intense investigations but still poorly understood. For instance, the derivation of Fourier law in Hamiltonian systems is a problem that still poses several obstacles. In order to investigate…
Path-dependent stochastic processes are often non-ergodic and observables can no longer be computed within the ensemble picture. The resulting mathematical difficulties pose severe limits to the analytical understanding of path-dependent…
Calculating the Shannon entropy for symbolic sequences has been widely considered in many fields. For descriptive statistical problems such as estimating the N-gram entropy of English language text, a common approach is to use as much data…
This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…
In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…
We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our…
Ergodic properties and asymptotic stationarity are investigated in this paper for the pseudo-covariance matrix (PCM) of a recursive state estimator which is robust against parametric uncertainties and is based on plant output measurements…
Nowadays many tools, e.g. fluctuation relations, are available to characterize the statistical properties of non-equilibrium systems. However, most of these tools rely on the assumption that the driving noise is normally distributed. Here…
In queuing theory and related problems, it is very important to know the numerical characteristics of an investigated system - both in stationary and non-stationary modes. In some cases, such characteristics can be calculated, but this is…