Related papers: Bridges of Markov counting processes. Reciprocal c…
Two approaches to studying the correlation functions of the binary Markov sequences are considered. The first of them is based on the study of probability of occurring different ''words'' in the sequence. The other one uses recurrence…
In this paper the class of mixed renewal processes (MRPs for short) with mixing parameter a random vector from \cite{lm6z3} (enlarging Huang's \cite{hu} original class) is replaced by the strictly more comprising class of all extended MRPs…
Changing time of simple continuous-time Markov counting processes by independent unit-rate Poisson processes results in Markov counting processes for which we provide closed-form transition rates via composition of trajectories and with…
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…
It is well-known that well-posedness of a martingale problem in the class of continuous (or r.c.l.l.) solutions enables one to construct the associated transition probability functions. We extend this result to the case when the martingale…
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…
We present a theorem which elucidates the connection between self-duality of Markov processes and representation theory of Lie algebras. In particular, we identify sufficient conditions such that the intertwining function between two…
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 introduce Markov substitute processes, a new model at the crossroad of statistics and formal grammars, and prove its main property : Markov substitute processes with a given support form an exponential family.
For a Markov chain both the detailed balance condition and the cycle Kolmogorov condition are algebraic binomials. This remark suggests to study reversible Markov chains with the tool of Algebraic Statistics, such as toric statistical…
In this paper we present elementary computations for some Markov modulated counting processes, also called counting processes with regime switching. Regime switching has become an increasingly popular concept in many branches of science. In…
The conditionally Markov (CM) sequence contains several classes, including the reciprocal sequence. Reciprocal sequences have been widely used in many areas of engineering, including image processing, acausal systems, intelligent systems,…
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. In this…
Recently Belopolskaya and Suhov studied Markov process's in a random environment, where the environment changes in likeness to a Markov process. Constructions were made to allow the process to "interact with the environment", this was done…
Exchangeable sequences of random probability measures (partitions of mass) and their corresponding exchangeable bridges play an important role in a variety of areas in probability, statistics and related areas, including Bayesian…
Causal reversibility blends reversibility and causality for concurrent systems. It indicates that an action can be undone provided that all of its consequences have been undone already, thus making it possible to bring the system back to a…
For non-equilibrium systems described by finite Markov processes, we consider the number of times that a system traverses a cyclic sequence of states (a cycle). The joint distribution of the number of forward and backward instances of any…
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…
Let X and Y be time-homogeneous Markov processes with common state space E, and assume that the transition kernels of X and Y admit densities with respect to suitable reference measures. We show that if there is a time t>0 such that, for…
Switches are operations which make local changes to the edges of a graph, usually with the aim of preserving the vertex degrees. We study a restricted set of switches, called triangle switches. Each triangle switch creates or deletes at…