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This paper consider a highly general dissemination model that keeps track of the stochastic evolution of the distribution of wealth over a set of agents. There are two types of events: (i) units of wealth externally arrive, and (ii) units…
A Markov network characterizes the conditional independence structure, or Markov property, among a set of random variables. Existing work focuses on specific families of distributions (e.g., exponential families) and/or certain structures…
A one-dimensional Ising model with nearest neighbour interactions is applied to study compaction processes in granular media. An equivalent particle-hole picture is introduced, with the holes being associated to the domain walls of the…
In this short note we investigate the natur of the phase transitions in a spin market model as a function of the interaction strength between local and global effects. We find that the stochastic dynamics of this stylized market model…
Hidden semi-Markov models generalise hidden Markov models by explicitly modelling the time spent in a given state, the so-called dwell time, using some distribution defined on the natural numbers. While the (shifted) Poisson and negative…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
Network reliability is the probability that a dynamical system composed of discrete elements interacting on a network will be found in a configuration that satisfies a particular property. We introduce a new reliability property, Ising…
A discrete-time random process is described which can generate bursty sequences of events. A Bernoulli process, where the probability of an event occurring at time $t$ is given by a fixed probability $x$, is modified to include a memory…
We analyze infection spreading processes in a system where only a fraction $p$ of individuals can be affected by disease, while remaining $1-p$ individuals are immune. Such a picture can emerge as a natural consequence of previously…
An algorithm for the unbiased simulation of continuous max-(resp.\ min-)id stochastic processes is developed. The algorithm only requires the simulation of finite Poisson random measures on the space of continuous functions and avoids the…
This paper considers a distributed decision-making approach for manufacturing task assignment and condition-based machine health maintenance. Our approach considers information sharing between the task assignment and health management…
We adapt a fitness function from evolutionary game theory as a mechanism for aggregation and dispersal in a partial differential equation (PDE) model of two interacting populations, described by density functions $u$ and $v$. We consider a…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
We study the distribution of the maximum of a set of random fitnesses with fixed number of mutations in a model of biological evolution. The fitness variables are not independent and the correlations can be varied via a parameter…
A key issue in the control of distributed discrete systems modeled as Markov decisions processes, is that often the state of the system is not directly observable at any single location in the system. The participants in the control scheme…
We introduce the effect of site contamination in a model for spatial epidemic spread and show that the presence of site contamination may have a strict effect on the model in the sense that it can make an otherwise subcritical process…
We study the stability properties of a susceptible-infected-susceptible (SIS) diffusion model, so-called the $n$-intertwined Markov model, over arbitrary directed network topologies. As in the majority of the work on infection spread…
Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach…
We study here the dynamics (and stability) of Probabilistic Population Protocols, via the differential equations approach. We provide a quite general model and we show that it includes the model of Angluin et. al. in the case of very large…