Related papers: Martin Capacity for Markov Chains

From the datum of an integer partition and a classical Lie algebra, one can define a Markov chain on an associated multiplicative graph. For each classical family A, C, B, D, we thus obtain a sequence of Markov chain which is indexed by the…

Let T be a measurable transformation of a probability space $(E,\mathcal {E},\pi)$, preserving the measure {\pi}. Let X be a random variable with law \pi. Call K(\cdot, \cdot) a regular version of the conditional law of X given T(X). Fix…

In this article we study stability properties of $g_O$, the standard Green kernel for $O$ an open regular set in $R^d$. In $d\ge 3$ we show that $g_O^\beta$ is again a Green kernel of a Markov Feller process, for any power $\beta\in…

An analytical formula for the occurence probability of Markovian stochastic paths with repeatedly visited and/or equal departure rates is derived. This formula is essential for an efficient investigation of the trajectories belonging to…

Let $\{X_n\}_{n\in\N}$ be a Markov chain on a measurable space $\X$ with transition kernel $P$ and let $V:\X\r[1,+\infty)$. The Markov kernel $P$ is here considered as a linear bounded operator on the weighted-supremum space $\cB_V$…

Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically.…

Random walks on simple graphs in connection with electrical resistor networks lead to the definition of Markov chains with transition probability matrix in terms of electrical conductances. We extend this definition to an effective…

We study a space-time Brownian motion with drift B(t)=(t_0+t,y_0+W(t)+t) killed at the moving boundary of the cone {(t,x):0<x<t}. This article determines the parabolic Martin boundary and all harmonic functions associated with this process.…

Let T be an infinite homogenous tree of homogeneity $q+1$. Attaching to each edge the conductance $1$, the tree will became an electric network. The reversible Markov chain associated to this network is the simple random walk on the…

Computational procedures for the stationary probability distribution, the group inverse of the Markovian kernel and the mean first passage times of an irreducible Markov chain, are developed using perturbations. The derivation of these…

We construct a bounded degree graph $G$, such that a simple random walk on it is transient but the random walk path (i.e., the subgraph of all the edges the random walk has crossed) has only finitely many cutpoints, almost surely. We also…

We study group-averaged Markov chains obtained by augmenting a $\pi$-stationary transition kernel $P$ with a group action on the state space via orbit kernels. Given a group $\mathcal{G}$ with orbits $(\mathcal{O}_i)_{i=1}^k$, we analyse…

The transition matrix of a Markov chain $(X_k,k\geq 0)$ on a finite or infinite rooted tree is said to be almost upper-directed if, given $X_k$, the node $X_{k+1}$ is either a descendant of $X_k$ or the parent of $X_k$. It is said to be…

R\'emy's algorithm is a Markov chain that iteratively generates a sequence of random trees in such a way that the $n^{\mathrm{th}}$ tree is uniformly distributed over the set of rooted, planar, binary trees with $2n+1$ vertices. We obtain a…

The cover time of a Markov chain on a finite state space is the expected time until all states are visited. We show that if the cover time of a discrete-time Markov chain with rational transitions probabilities is bounded, then it is a…

We consider the motion of a particle on a Galton Watson tree, when the probabilities of jumping from a vertex to any one of its neighbours is determined by a random process. Given the tree, positive weights are assigned to the edges in such…

In this paper we develop a statistical estimation technique to recover the transition kernel $P$ of a Markov chain $X=(X_m)_{m \in \mathbb N}$ in presence of censored data. We consider the situation where only a sub-sequence of $X$ is…

We extend the conductance and canonical paths methods to the setting of general finite Markov chains, including non-reversible non-lazy walks. The new path method is used to show that a known bound for mixing time of a lazy walk on a Cayley…

A discrete-time Markov chain can be transformed into a new Markov chain by looking at its states along iterations of an almost surely finite stopping time. By the optional stopping theorem, any bounded harmonic function with respect to the…

It is shown that transient graphs for the simple random walk do not admit a nearest neighbor transient Markov chain (not necessarily a reversible one), that crosses all edges with positive probability, while there is such chain for the…