A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential...

the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain...

In probability, a discrete-time Markov chain (DTMC) is a sequence of random variables, known as a stochastic process, in which the value of the next variable...

equations characterize continuous-time Markov processes. In particular, they describe how the probability of a continuous-time Markov process in a certain...

processes, such as Markov chains and Poisson processes, can be derived as special cases among the class of Markov renewal processes, while Markov renewal processes...

from its connection to Markov chains, a concept developed by the Russian mathematician Andrey Markov. The "Markov" in "Markov decision process" refers...

Absorbing Markov chain Continuous-time Markov chain Discrete-time Markov chain Nearly completely decomposable Markov chain Quantum Markov chain Telescoping...

and sufficient condition for a Markov chain or continuous-time Markov chain to be stochastically identical to its time-reversed version. The theorem states...

2,3,...}. This is the same continuous time Markov chain as in a birth–death process. The state space diagram for this chain is as below. The model is considered...

"Probability distributions of the Kolmogorov and omega-square statistics for continuous distributions with shift and scale parameters". Journal of Soviet Mathematics...

}}X(t)>0\\\max(r_{i},0)&{\text{ if }}X(t)=0.\end{cases}}} The operator is a continuous time Markov chain and is usually called the environment process, background process...

theory, a Markov reward model or Markov reward process is a stochastic process which extends either a Markov chain or continuous-time Markov chain by adding...

constructing such Markov chains, including the Metropolis–Hastings algorithm. Markov chain Monte Carlo methods create samples from a continuous random variable...

criterion defines the condition for a Markov chain or continuous-time Markov chain to be time-reversible. Time reversal of numerous classes of stochastic...

Discrete-time Markov chain § Stationary distributions and continuous-time Markov chain § Stationary distribution, a special distribution for a Markov chain such...

array of numbers describing the instantaneous rate at which a continuous-time Markov chain transitions between states. In a transition-rate matrix Q {\displaystyle...

once entered, cannot be left. Like general Markov chains, there can be continuous-time absorbing Markov chains with an infinite state space. However, this...

is a method for the analysis of quasi-birth–death processes, continuous-time Markov chain whose transition rate matrices with a repetitive block structure...

generator matrix, of a continuous time Markov chain, a class of stochastic processes Infinitesimal generator of a strongly continuous semigroup This disambiguation...

examples of Markov chains and Markov processes in action. All examples are in the countable state space. For an overview of Markov chains in general state...

of customers it can contain. The model can be described as a continuous time Markov chain with transition rate matrix Q = ( − λ λ μ − ( μ + λ ) λ 2 μ −...

A hidden Markov model (HMM) is a Markov model in which the observations are dependent on a latent (or hidden) Markov process (referred to as X {\displaystyle...

jumps interspersed with small continuous movements. Poisson process, an example of a jump process Continuous-time Markov chain (CTMC), an example of a jump...

space of some continuous-time Markov chains, first published by Kemeny and Snell. Suppose that the complete state-space of a Markov chain is divided into...

definition of a Markov chain varies. For example, it is common to define a Markov chain as a Markov process in either discrete or continuous time with a countable...

substitution across sites. Continuous-time Markov chains have the usual transition matrices which are, in addition, parameterized by time, t {\displaystyle t}...

any stationary distribution) of a Markov chain, when such a distribution exists. For a continuous time Markov chain with state space S {\displaystyle...

The block matrix Q below is a transition rate matrix for a continuous-time Markov chain. Q = [ D 0 D 1 0 0 … 0 D 0 D 1 0 … 0 0 D 0 D 1 … ⋮ ⋮ ⋱ ⋱ ⋱ ]...

H. A. Davis in 1984. Piecewise linear models such as Markov chains, continuous-time Markov chains, the M/G/1 queue, the GI/G/1 queue and the fluid queue...

Robinson's Non-Standard Analysis. Consider the embedded Markov chain of the M/G/1 queue, where the time points selected are immediately after the moment of...