We review recent theoretical works that enable the accurate evaluation of the mean first passage time (MFPT) of a random walker to a target in confinement for Markovian (memory-less) and non-Markovian walkers. For the Markovian problem, we present a general theory which allows one to accurately evaluate the MFPT and its extensions to related first-passage observables such as splitting probabili...

Markovian testing and trace equivalences have been recently proposed as reasonable alternatives to Markovian bisimilarity, as both of them induce at the Markov chain level an aggregation strictly coarser than ordinary lumping that is still exact. In this paper we provide a modal logic characterization for each of the two non-bisimulation-based Markovian behavioral equivalences, which relies on ...

the stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use markovian jumps to model stochastic reaction diffusion systems‎. ‎in this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with markovian jumps‎. ‎under some reasonable conditions‎, ‎we show that the trivial solution of stocha...

Abstract We provide a quantitative evaluation of non-Markovianity (NM) for an XX chain interacting qubits with one end coupled to reservoir. The NM several non-Markovian spectral densities is assessed in terms various quantum state distance (QSD) measures. Our approach based on the construction density matrix open chain, without necessity master
equation. For quantification we calculate...

we compare two approaches for a markovian model in flexible manufacturing systems (fmss) using monte carlo simulation. the model which is a development of fazlollahtabar and saidi-mehrabad (2013), considers two features of automated flexible manufacturing systems equipped with automated guided vehicle (agv) namely, the reliability of machines and the reliability of agvs in a multiple agv jobsho...

Probabilistic Boolean Networks, which form a subclass of Markovian Genetic Regulatory Networks, have been recently introduced as a rule-based paradigm for modeling gene regulatory networks. In an earlier paper, we introduced external control into Markovian Genetic Regulatory networks. More precisely, given a Markovian genetic regulatory network whose state transition probabilities depend on an ...

A rigorous formalism for the extraction of state-to-state transition functions from a Boltzmann-weighted ensemble of microcanonical molecular dynamics simulations has been developed as a way to study the kinetics of protein folding in the context of a Markov chain. Analysis of these transition functions for signatures of Markovian behavior is described. The method has been applied to an example...

Since the advent of Markovian Process Algebras, users have requested the ability to employ a greater variety of action distribution. We present a conservative extension to the popular Markovian process algebra, PEPA, which incorporates generally distributed sojourn-times for action duration. Just as a PEPA model generates a Markov chain for analysis purposes, so semi-Markov PEPA produces a semi...

How many times should a card shuffler shuffle to get the cards shuffled? Convergence rate questions like these are central to the theory of finite Markov Chains and arise in diverse fields including Physics, Computer Science as well as Biology. This thesis introduces two new approaches to estimating mixing times: robust mixing time of a Markov Chain and Markovian product of Markov Chains. The “...

How many times should a card shuffler shuffle to get the cards shuffled? Convergence rate questions like these are central to the theory of finite Markov Chains and arise in diverse fields including Physics, Computer Science as well as Biology. This thesis introduces two new approaches to estimating mixing times: robust mixing time of a Markov Chain and Markovian product of Markov Chains. The “...