相关论文: Hidden Markov Process: A New Representation, Entro…

Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…

The formalism of state estimation and hidden Markov models (HMMs) can simplify and clarify the discussion of stochastic thermodynamics in the presence of feedback and measurement errors. After reviewing the basic formalism, we use it to…

The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…

Sequential data modeling and analysis have become indispensable tools for analyzing sequential data, such as time-series data, because larger amounts of sensed event data have become available. These methods capture the sequential structure…

Speed limit for classical stochastic Markov processes with discrete states is studied. We find that a trade-off inequality exists between the speed of the state transformation and the entropy production. The dynamical activity determines…

When is keeping a memory of observations worthwhile? We use hidden Markov models to look at phase transitions that emerge when comparing state estimates in systems with discrete states and noisy observations. We infer the underlying state…

The reflected entropy $S_R(A:B)$ of a density matrix $\rho_{AB}$ is a bipartite correlation measure lower-bounded by the quantum mutual information $I(A:B)$. In holographic states satisfying the quantum extremal surface formula, where the…

Let $P_n$ and $Q_n$ be two probability measures representing two different probabilistic models of some system (e.g., an $n$-particle equilibrium system, a set of random graphs with $n$ vertices, or a stochastic process evolving over a time…

We focus on a data sequence produced by repetitive quantum measurement on an internal hidden quantum system, and call it a hidden Markovian process. Using a quantum version of the Perron-Frobenius theorem, we derive novel upper and lower…

This paper studies the synthesis of an active perception policy that maximizes the information leakage of the initial state in a stochastic system modeled as a hidden Markov model (HMM). Specifically, the emission function of the HMM is…

We show for Markov diffusion processes that the quadratic entropic bound, recently derived for the rate functions of nonequilibrium currents, can be seen as being produced by an effective process that creates current fluctuations in a…

In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…

We study finite state random dynamical systems (RDS) and their induced Markov chains (MC) as stochastic models for complex dynamics. The linear representation of deterministic maps in RDS are matrix-valued random variables whose…

We introduce a natural way of visualizing the entropy production in heat transfer processes between a system and a thermal reservoir. This representation is particularly useful to highlight the asymmetric character of the heating and…

This paper addresses the challenge of a particular class of noisy state observations in Markov Decision Processes (MDPs), a common issue in various real-world applications. We focus on modeling this uncertainty through a confusion matrix…

Current research in statistical mechanics mostly concerns the investigation of out-of-equilibrium, irreversible processes, which are ubiquitous in nature and still far from being theoretically understood. Even the precise characterization…

We observe an infinite sequence of independent identically distributed random variables $X_1,X_2,\ldots$ drawn from an unknown distribution $p$ over $[n]$, and our goal is to estimate the entropy $H(p)=-\mathbb{E}[\log p(X)]$ within an…

We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for…

Transfer entropy (TE) was introduced by Schreiber in 2000 as a measurement of the predictive capacity of one stochastic process with respect to another. Originally stated for discrete time processes, we expand the theory in line with recent…

In this article, relying on Foster-Lyapunov drift conditions, we establish subexponential upper and lower bounds on the rate of convergence in the $\mathrm{L}^p$-Wasserstein distance for a class of irreducible and aperiodic Markov…