Related papers: Pair correlation functions and limiting distributi…
We consider several special cases of iterations of random i.i.d. linear functions with beta distributed fixed points that generate nested interval schemes when iterated in a backward direction, and ergodic Markov chains in the forward…
We introduce a framework to approximate a Markov Decision Process that stands on two pillars: state aggregation -- as the algorithmic infrastructure; and central-limit-theorem-type approximations -- as the mathematical underpinning of…
The definition and the properties of a Gaussian point distribution, in contrast to the well-known properties of a Gaussian random field are discussed. Constraints for the number density and the two-point correlation function arise. A simple…
Markov chains for probability distributions related to matrix product states and 1D Hamiltonians are introduced. With appropriate 'inverse temperature' schedules, these chains can be combined into a random approximation scheme for ground…
We study the classical occupancy problem from the viewpoint of its embedding Markov chain. We derive new expressions for the probability mass function and (complementary) distribution function in generalized form. Furthermore, we derive a…
In this paper we propose a (sub)distribution-based bisimulation for labelled Markov processes and compare it with earlier definitions of state and event bisimulation, which both only compare states. In contrast to those state-based…
We construct a Markov process model to describe the evolution of labor division and its dynamical behavior is investigated by numerical simulations in detail. We have shown that under the mechanism of increasing returns, the division of…
We prove two propositions with conditions that a system, which is described by a transient Markov chain, will display local stability. Examples of such systems include partly overloaded Jackson networks, partly overloaded polling systems,…
A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat Kotecky-Preiss criterion. Expressions and estimates for correlation functions are…
The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, reproduce and die independently and, with a probability that…
Given a description of the stacking statistics of layered close-packed structures in the form of a hidden Markov model, we develop analytical expressions for the pairwise correlation functions between the layers. These may be calculated…
We study quasi-stationary distributions and quasi-limiting behavior of Markov chains in general reducible state spaces with absorption. We propose a set of assumptions dealing with particular situations where the state space can be…
Continuous-time Markov chains describing interacting processes exhibit a state space that grows exponentially in the number of processes. This state-space explosion renders the computation or storage of the time-marginal distribution, which…
It is shown that in equilibrium a canonical ensemble of particles with two-particle interaction the Gibbs distribution function may be expressed uniquely through a pair distribution function. It means, that for given values of the particle…
We give a sufficient condition for a random sequence in [0,1] generated by a $\Psi$-process to be equidistributed. The condition is met by the canonical example -- the $\max$-2 process -- where the $n$th term is whichever of two uniformly…
In the continuity of a recent paper ([6]), dealing with finite Markov chains, this paper proposes and analyzes a recursive algorithm for the approximation of the quasi-stationary distribution of a general Markov chain living on a compact…
Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…
It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of…
We consider almost upper semi-continuous processes defined on a finite Markov chain. The distributions of the functionals associated with the exit from a finite interval are studied. We also consider some modification of these processes.
We develop a model for credit rating migration that accounts for the impact of economic state fluctuations on default probabilities. The joint process for the economic state and the rating is modelled as a time-homogeneous Markov chain.…