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Here the service time distribution is no longer a Markov process.
Markov processes have been used to model and study this type of system.
He became well known for his contributions on time series and Markov processes.
This talk was titled "Markov processes and problems in analysis".
He also produced important papers on the general theory of Markov processes.
A process with this property is called a Markov process.
The entropy growth in all Markov processes was explicitly proved later.
It is a continuous-time Markov process with almost surely continuous sample paths.
Each of the states of the Markov process represents one of the phases.
The contraction semigroup case is widely used in the theory of Markov processes.
If is the generator of a Markov process as explained before, we can give a general solution to (3.2):
In particular, this condition is valid for all Markov processes without any relation to time-reversibility.
The phase-type distribution is the time to absorption of a finite state Markov process.
In probability theory, semigroups are associated with Markov processes .
Because r is governed by a Markov process, dynamic programming simplifies the problem significantly.
The first product-form solutions were found for equilibrium distributions of Markov processes.
Assume that is a (homogeneous) continuous time Markov process taking values in .
The random walk is well-defined in random processes with the Markov process model.
The syntactic probabilities are modelled by a first order Markov process:
If represents the total value of the coins set on the table after n draws, with , then the sequence is not a Markov process.
Formally it has to be of the order of the autocorrelation time of the Markov process.
The distribution can be represented by a random variable describing the time until absorption of a Markov process with one absorbing state.
If represents the number of dollars you have in chips after n tosses, with , then the sequence is a Markov process.
The most famous Markov process is a Markov chain.
Brownian motion is another well-known Markov process.