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There is a well-established theory linking certain semi-Markov chains and continuous-time random walks to time-fractional equations and anomalous diffusion. In this work, we go beyond the semi-Markov framework by considering some…

We introduce the notion of empirical coordination for quantum correlations. Quantum mechanics enables the calculation of probabilities for experimental outcomes, emphasizing statistical averages rather than detailed descriptions of…

The formal verification of large probabilistic models is important and challenging. Exploiting the concurrency that is often present is one way to address this problem. Here we study a restricted class of asynchronous distributed…

Markov decision processes are typically used for sequential decision making under uncertainty. For many aspects however, ranging from constrained or safe specifications to various kinds of temporal (non-Markovian) dependencies in task and…

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…

The basic question in perturbation analysis of Markov chains is: how do small changes in the transition kernels of Markov chains translate to chains in their stationary distributions? Many papers on the subject have shown, roughly, that the…

The paper studies closed queueing networks containing a server station and $k$ client stations. The server station is an infinite server queueing system, and client stations are single-server queueing systems with autonomous service, i.e.…

We study time-changed Markov processes to speed up the convergence of Markov chain Monte Carlo (MCMC) algorithms. The time-changed process is defined by adjusting the speed of time of a base process via a user-chosen, state-dependent…

In many complex systems, elements interact via time-varying network topologies. Recent research shows that temporal correlations in the chronological ordering of interactions crucially influence network properties and dynamical processes.…

We study normal approximations for a class of discrete-time occupancy processes, namely, Markov chains with transition kernels of product Bernoulli form. This class encompasses numerous models which appear in the complex networks…

For Markov jump processes on irreducible networks with finite number of sites, we derive a general and explicit expression of the squared coefficient of variation for the net number of transitions from one site to a connected site in a…

Markov processes are popular mathematical models, studied by theoreticians for their intriguing properties, and applied by practitioners for their flexible structure. With this book we teach how to model and analyze Markov processes. We…

Many systems across the sciences evolve through a combination of multiplicative growth and diffusive transport. In the presence of disorder, these systems tend to form localized structures which alternate between long periods of relative…

A general formalism is introduced to allow the steady state of non-Markovian processes on networks to be reduced to equivalent Markovian processes on the same substrates. The example of an epidemic spreading process is considered in detail,…

We study the properties of a subclass of stochastic processes called discrete time nonlinear Markov chains with an aggregator, which naturally appear in various topics such as strategic queueing systems, inventory dynamics, opinion…

Many empirical studies have revealed that the occurrences of contacts associated with human activities are non-Markovian temporal processes with a heavy tailed inter-event time distribution. Besides, there has been increasing empirical…

The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily…

We introduce and study a family of Markov processes on partitions. The processes preserve the so-called z-measures on partitions previously studied in connection with harmonic analysis on the infinite symmetric group. We show that the…

We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method for resolution of equations, included…

This article examines the queueing performance of communication systems that transmit encoded data over unreliable channels. A fading formulation suitable for wireless environments is considered where errors are caused by a discrete channel…