We study the stochastic dynamics of a system interacting species in environment by means continuous-time Markov chain with transition rates depending on state environment. Models gene regulation systems biology take this form. characterise finite-time distribution chain, provide conditions for ergodicity, and stationary (when it exists) as mixture Poisson distributions. The measure is uniquely ...

We study the probabilistic safety verification problem for pure jumpMarkov processes, a class of models that generalizes continuous-time Markov chains over continuous (uncountable) state spaces. Solutions of these processes are piecewise constant, right-continuous functions from time to states. Their jump (or reset) times are realizations of a Poisson process, characterized by a jump rate funct...

Traditional queueing theory deals mainly with one-dimensional stochastic processes like queue or orbit length, virtual or actual waiting or sojourn time, busy period, etc. Discrete or continuous time one-dimensional Markov chains and renewal theory are the main tools for their investigation. However, the increasing complexity of the modern telecommunication networks (heterogeneous bursty correl...

We study new formulae based on Lyapunov exponents for entropy, mutual information, and capacity of finite state discrete time Markov channels. We also develop a method for directly computing mutual information and entropy using continuous state space Markov chains. Our methods allow for arbitrary input processes and channel dynamics, provided both have finite memory. We show that the entropy ra...

The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to I.Ibragimov and R.Khasminskii [14], consistency, asymptotic normality and convergence of moments are established for MLE under certain strong ergodicity conditions o...

We study new formulas based on Lyapunov exponents for entropy, mutual information, and capacity of finite state discrete time Markov channels. We also develop a method for directly computing mutual information and entropy using continuous state space Markov chains. Our methods allow for arbitrary input processes and channel dynamics, provided both have finite memory. We show that the entropy ra...