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...

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

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...

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

In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution...

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

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...

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

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

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...

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...

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...

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

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

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...

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

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

process is a special case of a continuous-time Markov process and a generalisation of a Poisson process. It defines a continuous process which takes values...

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

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

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

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 −...

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

random walks is through continuous-time Markov chains. Unlike the coin-based mechanism used in discrete-time random walks, Markov chains do not rely on a coin...

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

}}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...

network schedulers in computing. As the term is generally used, time slices (also known as time quanta) are assigned to each process in equal portions and...

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 … ⋮ ⋮ ⋱ ⋱ ⋱ ]...

stationary continuous-time Markov chain, a process defined as the time-reversed process has the same stationary distribution as the forward-time process...