Related papers: Ergodicity of Random Walks on Random DFA

We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now…

The cutoff phenomenon describes a sharp transition in the convergence of an ergodic finite Markov chain to equilibrium. Of particular interest is understanding this convergence for the simple random walk on a bounded-degree expander graph.…

A random-walk Metropolis sampler is geometrically ergodic if its equilibrium density is super-exponentially light and satisfies a curvature condition [Stochastic Process. Appl. 85 (2000) 341-361]. Many applications, including Bayesian…

In this paper, we study dynamical properties as hypercyclicity, supercyclicity, frequent hypercyclicity and chaoticity for transition operators associated to countable irreductible Markov chains. As particular cases, we consider simple…

Let {X_n,n\geq0} be a Markov chain on a general state space X with transition probability P and stationary probability \pi. Suppose an additive component S_n takes values in the real line R and is adjoined to the chain such that…

In the simplest sequential decision problem for an ergodic stochastic process X, at each time n a decision u_n is made as a function of past observations X_0,...,X_{n-1}, and a loss l(u_n,X_n) is incurred. In this setting, it is known that…

Fix an irrational number $\alpha$ and a smooth, positive, real function $\mathfrak{p}$ on the circle. If current position is $x\in \mathbb R/\mathbb Z$ then in the next step jump to $x+\alpha$ with probability $\mathfrak{p}(x)$ or to…

We study the ergodic property of a continuous-state branching process with immigration and competition. The exponential ergodicity in a weighted total variation distance is proved under natural assumptions. The main theorem applies to…

In ergodic physical systems, time-averaged quantities converge (for large times) to their ensemble-averaged values. Large deviation theory describes rare events where these time averages differ significantly from the corresponding ensemble…

Famously, a $d$-dimensional, spatially homogeneous random walk whose increments are non-degenerate, have finite second moments, and have zero mean is recurrent if $d \in \{1,2\}$ but transient if $d \geq 3$. Once spatial homogeneity is…

It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information. While the existing theory provides a rather complete picture…

In this paper, we study nonlocal random walk strategies generated with the fractional Laplacian matrix of directed networks. We present a general approach to analyzing these strategies by defining the dynamics as a discrete-time Markovian…

The rotor walk on a graph is a deterministic analogue of random walk. Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits. We consider rotor walk on an…

We consider a Metropolis--Hastings method with proposal $\mathcal{N}(x, hG(x)^{-1})$, where $x$ is the current state, and study its ergodicity properties. We show that suitable choices of $G(x)$ can change these compared to the Random Walk…

Let $G$ be a connected semisimple real Lie group with finite center, and $\mu$ a probability measure on $G$ whose support generates a Zariski-dense subgroup of $G$. We consider the right $\mu$-random walk on $G$ and show that each random…

In this paper, we present an overview of different types of random walk strategies with local and non-local transitions on undirected connected networks. We present a general approach to analyzing these strategies by defining the dynamics…

Consider a random walk whose (light-tailed) increments have positive mean. Lower and upper bounds are provided for the expected maximal value of the random walk until it experiences a given drawdown d. These bounds, related to the Calmar…

Network meta-analysis (NMA) is a central tool for evidence synthesis in clinical research. The results of an NMA depend critically on the quality of evidence being pooled. In assessing the validity of an NMA, it is therefore important to…

We are concerned with the absolute continuity of stationary distributions corresponding to some piecewise deterministic Markov process, being typically encountered in biological models. The process under investigation involves a…

We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…