Related papers: Chains of infinite order, chains with memory of va…

We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general H\"older observables fail. We obtain limit laws for such maps and H\"older…

Variable Length Memory Chains (VLMC), which are generalizations of finite order Markov chains, turn out to be an essential tool to modelize random sequences in many domains, as well as an interesting object in contemporary probability…

In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…

Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a…

We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…

The aim of this note is to construct a probability measure on the space of trajectories in a continuous time Markov chain having a finite state diagram, or more generally which admits a global bound on its degree and rates. Our approach is…

A method of constructing Markov chains on finite state spaces is provided. The chain is specified by three constraints: stationarity, dependence and marginal distributions. The generalized Pythagorean theorem in information geometry plays a…

In this note we complete the analysis carried on in \cite{CGSV} about the topological synchronisation of unimodal maps of the interval coupled in a master-slave configuration, by answering to the questions raised in that paper. Namely, we…

It is shown that a seemingly harmless reordering of the steps in a block Gibbs sampler can actually invalidate the algorithm. In particular, the Markov chain that is simulated by the "out-of-order" block Gibbs sampler does not have the…

We study continuous-time Markov chains on the non-negative integers under mild regularity conditions (in particular, the set of jump vectors is finite and both forward and backward jumps are possible). Based on the so-called flux balance…

Stochastic chains with memory of variable length constitute an interesting family of stochastic chains of infinite order on a finite alphabet. The idea is that for each past, only a finite suffix of the past, called context, is enough to…

We consider the higher-order Markov Chain, and characterize the second order Markov chains admitting every probability distribution vector as a stationary vector. The result is used to construct Markov chains of higher-order with the same…

We establish convergence to an invariant measure as time tends to infinity, for a large class of (possibly non-Markovian) stochastic volatility models. Our arguments are based on a novel coupling idea for Markov chains which also extends to…

The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain. The simulations of this stochastic process and its invariant measure are…

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

We investigate multivariate regular variation in the context of time-homogeneous Markov chains on general vector spaces and in random coefficient linear models. In the first part, we show that the regular variation of the stationary…

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…

The main goal of the paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate a decomposition procedure for the…

We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…

A new object of the probability theory, two-sided chain of events (symbols), is introduced. A theory of multi-steps Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to establish…