Related papers: Exchangeable Markov processes on graphs: Feller ca…
We define and study a family of Markov processes with state space the compact set of all partitions of N that we call exchangeable fragmentation-coalescence processes. They can be viewed as a combination of exchangeable fragmentation as…
We consider a finite-state, continuous-time Markov process, represented in the "linear framework" by a directed graph with labelled edges which specifies the infinitesimal generator of the process. If the graph is strongly connected, the…
The Feller property concerns the preservation of the space of functions vanishing at infinity by the semigroup generated by an operator. We study this property in the case of the Laplacian on infinite graphs with arbitrary edge weights and…
A classification for Brownian motions on metric graphs, that is, right continuous strong Markov processes which behave like a one-dimensional Brownian motion on the edges and feature effects like Walsh skewness, stickiness and jumps at the…
Let X and Y be time-homogeneous Markov processes with common state space E, and assume that the transition kernels of X and Y admit densities with respect to suitable reference measures. We show that if there is a time t>0 such that, for…
A time and space inhomogeneous Markov process is a Feller evolution process, if the corresponding evolution system on the continuous functions vanishing at infinity is strongly continuous. We discuss generators of such systems and show that…
Brownian motions on a metric graph are defined, their Feller property is proved, and their generators are characterized. This yields a version of Feller's theorem for metric graphs.
We show that the (Gurevich) topological entropy for the countable Markov shift associated with an infinite transition matrix $A$ coincides with the non-commutative topological entropy for the Exel--Laca algebra associated with $A$, under…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…
We consider diffusion processes on metric graphs with semipermeable sticky membranes in each vertex. We prove that the process is governed by a Feller semigroup and find its asymptotic behavior as diffusion's speed increases to infinity…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes with Incomplete Information and with semi-uniform Feller transition probabilities. The important…
We propose a path transformation which applied to a cyclically exchangeable increment process conditions its minimum to belong to a given interval. This path transformation is then applied to processes with start and end at zero. It is seen…
We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the…
In this short paper, we connect the procedure of constructing a totally inaccessible stopping time for a given process using the well-known Cox construction, dependent on an independent exponential random variable; with naturally occurring…
We study Markov processes where the "time" parameter is replaced by paths in a directed graph from an initial vertex to a terminal one. Along each directed path the process is Markov and has the same distribution as the one along any other…
We characterise the convergence of a certain class of discrete time Markov processes toward locally Feller processes in terms of convergence of associated operators. The theory of locally Feller processes is applied to L\'evy-type processes…
We construct an infinitely exchangeable process on the set $\cate$ of subsets of the power set of the natural numbers $\mathbb{N}$ via a Poisson point process with mean measure $\Lambda$ on the power set of $\mathbb{N}$. Each $E\in\cate$…
Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question…