Related papers: Bisimulation for Feller-Dynkin Processes

The TASEP (totally asymmetric simple exclusion process) is a basic model for an one-dimensional interacting particle system with non-reversible dynamics. Despite the simplicity of the model it shows a very rich and interesting behaviour. In…

A classical approach to formal policy synthesis in stochastic dynamical systems is to construct a finite-state abstraction, often represented as a Markov decision process (MDP). The correctness of these approaches hinges on a behavioural…

We provide a systematic study of the notion of duality of Markov processes with respect to a function. We discuss the relation of this notion with duality with respect to a measure as studied in Markov process theory and potential theory…

Switched systems constitute an important modeling paradigm faithfully describing many engineering systems in which software interacts with the physical world. Despite considerable progress on stability and stabilization of switched systems,…

In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of…

In this paper, we introduce the notion of Bi-entangled hidden Markov processes. These are hidden quantum processes where the hidden processes themselves exhibit entangled Markov process, and the observable processes also exhibit…

Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…

In this short paper, we consider discrete-time Markov chains on lattices as approximations to continuous-time diffusion processes. The approximations can be interpreted as finite difference schemes for the generator of the process. We…

We quickly review labelled Markov processes (LMP) and provide a counterexample showing that in general measurable spaces, event bisimilarity and state bisimilarity differ in LMP. This shows that the logic in Desharnais [*] does not…

Time-delay systems are an important class of dynamical systems which provide a solid mathematical framework to deal with many application domains of interest ranging from biology, chemical, electrical, and mechanical engineering, to…

Diffusive approximations of Markov jump processes often fail to accurately capture large fluctuations. This is confounding, as the rare events triggered by these large fluctuations, such as the failure of electronic memories, are often the…

We present a new method of modelling numerical systems where there are two distinct output solution classes, for example tipping points or bifurcations. Gaussian process emulation is a useful tool in understanding these complex systems and…

A Markov decision process (MDP) is a state-based dynamical system capable of describing probabilistic behaviour with rewards. In this paper, we view MDPs as coalgebras living in the category of analytic spaces, a very general class of…

Bisimulations have been widely used in many areas of computer science to model equivalence between various systems, and to reduce the number of states of these systems, whereas uniform fuzzy relations have recently been introduced as a…

This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial…

In this paper the notion of bisimulation relation for linear input-state-output systems is extended to general linear differential-algebraic (DAE) systems. Geometric control theory is used to derive a linear-algebraic characterization of…

Game-theoretic characterizations of process equivalences traditionally form a central topic in concurrency; for example, most equivalences on the classical linear-time / branching-time spectrum come with such characterizations. Recent work…

Stuttering bisimulation is a well-known behavioral equivalence that preserves CTL-X, namely CTL without the next-time operator X. Correspondingly, the stuttering simulation preorder induces a coarser behavioral equivalence that preserves…

When two Markov operators commute, it suggests that we can couple two copies of one of the corresponding processes. We explicitly construct a number of couplings of this type for a commuting family of Markov processes on the set of…

Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is…