Related papers: Remarks on the multi-species exclusion process wit…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…
Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by…
In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…
A method for classifying $n$-species reaction-diffusion models, admitting shock solutions is presented. The most general one-dimensional two-species reaction-diffusion model with nearest neighbor interactions admitting uniform product…
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 general affine Markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup. We provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew…
We suggest a geometrical framework to discuss periodic layered structures in the unit disk. The band gaps appear when the point representing the system approaches the unit circle. We show that the trace of the matrix describing the basic…
We show that the joint probability generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of Markov processes called quadratic harnesses.…
This paper introduces a new approach of treating platoon systems using mean-variance control formulation. The underlying system is a controlled switching diffusion in which the random switching process is a continuous-time Markov chain.…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
We study the one-dimensional asymmetric simple exclusion process (ASEP) with open boundary conditions. Particles are injected and ejected at both boundaries. It is clarified that the steady state of the model is intimately related to the…
A class of exclusion processes in which particles perform history-dependent random walks is introduced, stimulated by dynamic phenomena in some biological and artificial systems. The particles locally interact with the underlying substrate…
Retrosynthesis planning is a fundamental challenge in chemistry which aims at designing reaction pathways from commercially available starting materials to a target molecule. Each step in multi-step retrosynthesis planning requires accurate…
The tail chain of a Markov chain can be used to model the dependence between extreme observations. For a positive recurrent Markov chain, the tail chain aids in describing the limit of a sequence of point processes $\{N_n,n\geq1\}$,…
We define the concept of an "open" Markov process, or more precisely, continuous-time Markov chain, which is one where probability can flow in or out of certain states called "inputs" and "outputs". One can build up a Markov process from…
The effects of a boundary on reaction systems are examined in the framework of the general single-species reaction/coalescence process. The boundary naturally represents the reactants' container, but is applicable to exciton dynamics in a…
Exclusion processes became paradigmatic models of nonequilibrium interacting particle systems of wide range applicability both across the natural and the applied, social and technological sciences. Usually they are defined as a…
This paper considers cluster detection in Block Markov Chains (BMCs). These Markov chains are characterized by a block structure in their transition matrix. More precisely, the $n$ possible states are divided into a finite number of $K$…
In this paper, we develop some matrix Poisson's equations satisfied by the mean and variance of the mixing time in an irreducible positive-recurrent discrete-time Markov chain with infinitely-many levels, and provide a computational…