Related papers: On Hidden Markov Processes with Infinite Excess En…

In any Markov chain with finite state space the distribution of transition records always belongs to the exponential family. This observation is used to prove a fluctuation theorem, and to show that the dynamical entropy of a stationary…

We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…

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 partial sum of the states of a Markov chain or more generally a Markov source is asymptotically normally distributed under suitable conditions. One of these conditions is that the variance is unbounded. A simple combinatorial…

We provide a large deviations analysis of deadlock phenomena occurring in distributed systems sharing common resources. In our model transition probabilities of resource allocation and deallocation are time and space dependent. The process…

We address the problem of detecting an anomalous process among a large number of processes. At each time t, normal processes are in state zero (normal state), while the abnormal process may be in either state zero (normal state) or state…

Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is…

In this paper we propose a model for open Markov chains that can be interpreted as a system of non-interacting particles evolving according to the rules of a Markov chain. The number of particles in the system is not constant, because we…

Markov decision processes continue to gain in popularity for modeling a wide range of applications ranging from analysis of supply chains and queuing networks to cognitive science and control of autonomous vehicles. Nonetheless, they tend…

Many natural and engineered systems can be modeled as discrete state Markov processes. Often, only a subset of states are directly observable. Inferring the conditional probability that a system occupies a particular hidden state, given the…

The study of Markov models is central to control theory and machine learning. A quantum analogue of partially observable Markov decision process was studied in (Barry, Barry, and Aaronson, Phys. Rev. A, 90, 2014). It was proved that…

We formally extend the notion of Markov order to open quantum processes by accounting for the instruments used to probe the system of interest at different times. Our description recovers the classical Markov order property in the…

Let X be a spectrally negative self-similar Markov process with 0 as an absorbing state. In this paper, we show that the distribution of the absorption time is absolutely continuous with an infinitely continuously differentiable density. We…

Memoryless processes are ubiquitous in nature, in contrast with the mathematics of open systems theory, which states that non-Markovian processes should be the norm. This discrepancy is usually addressed by subjectively making the…

For a certain class of isolated quantum systems, we report the existence of irreversible processes in which the energy is not dissipated. After a closed cycle in which the initial energy distribution is fully recovered, the expectation…

We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with…

We consider a stationary Markovian evolution with values on a disjointly partitioned set space $I\sqcup {\cal E}$. The evolution is visible (in the sense of knowing the transition probabilities) on the states in $I$ but not for the states…

The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…

In recent advances in finite-time thermodynamics, optimization of entropy production required for finite-time information processing is an important issue. In this work, we consider finite-time feedback processes in classical discrete…

Markovian memory embedded in a binary system is shaping its evolution on the basis of its current state and introduces either clustering or dispersion of binary states. The consequence is directly observed in the lengthening or shortening…