Related papers: Differential Entropy Rate Characterisations of Lon…
Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical…
In this work we present results about the rate of (relative) information loss induced by passing a real-valued, stationary stochastic process through a memoryless system. We show that for a special class of systems the information loss rate…
The limits of scaled relative entropies between probability distributions associated with N-particle weakly interacting Markov processes are considered. The convergence of such scaled relative entropies is established in various settings.…
The amount of information generated by a discrete time stochastic processes in a single step can be quantified by the entropy rate. We investigate the differences between two discrete time walk models, the discrete time quantum walk and the…
We present a new lower bound on the differential entropy rate of stationary processes whose sequences of probability density functions fulfill certain regularity conditions. This bound is obtained by showing that the gap between the…
We show that the dissipation rate bounds the rate at which physical processes can be performed in stochastic systems far from equilibrium. Namely, for rare processes we prove the fundamental tradeoff $\langle \dot S_\text{e} \rangle…
In this work, we investigate the relation between the concept of ``information rate'', an information geometric method for measuring the speed of the time evolution of the statistical states of a stochastic process, and stochastic…
The information detection of complex systems from data is currently undergoing a revolution, driven by the emergence of big data and machine learning methodology. Discovering governing equations and quantifying dynamical properties of…
We have shown how the intrinsic properties of a noise process can set an upper bound for the time derivative of entropy in a nonequilibrium system. The interplay of dissipation and the properties of noise processes driving the dynamical…
We prove a large deviation principle (LDP) and a fluctuation theorem (FT) for the entropy production rate (EPR) of the following $d$ dimensional stochastic differential equation \begin{equation*} d X_{t}=AX_{t} d t+\sqrt{Q} d B_{t}…
The goal of this paper is to develop an estimate for the entropy of random long-range correlated symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov…
For a Markov process the detailed balance condition is equivalent to the time-reversibility of the process. For stochastic differential equations (SDE's) time discretization numerical schemes usually destroy the property of…
We study the N-step binary stationary ergodic Markov chain and analyze its differential entropy. Supposing that the correlations are weak we express the conditional probability function of the chain through the pair correlation function and…
Finding parameters that minimise a loss function is at the core of many machine learning methods. The Stochastic Gradient Descent algorithm is widely used and delivers state of the art results for many problems. Nonetheless, Stochastic…
The presence of long-ranged correlations in a fluid undergoing uniform shear flow is investigated. An exact relation between the density autocorrelation function and the density-mometum correlation function implies that the former must…
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…
Entropy estimation, due in part to its connection with mutual information, has seen considerable use in the study of time series data including causality detection and information flow. In many cases, the entropy is estimated using…
Active matter systems operate far from equilibrium due to the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the…
We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic…
We obtain error terms on the rate of convergence to Extreme Value Laws for a general class of weakly dependent stochastic processes. The dependence of the error terms on the `time' and `length' scales is very explicit. Specialising to data…