Markov process
Noun
Meaning
a simple stochastic process in which the distribution of future states depends only on the present state and not on how it arrived in the present state
Source: WordNetSynonyms
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Examples
FTA: "It is natural to conjecture that the Markov process built in this way describes the Glauber dynamic of 33-dimensional ferromagnets near their critical temperature."
The value of T must be chosen according to different factors such as the proposal distribution and, formally, it has to be of the order of the autocorrelation time of the Markov process.
The Metropolis–Hastings algorithm involves designing a Markov process (by constructing transition probabilities) which fulfils the two above conditions, such that its stationary distribution π(x) is chosen to be P(x).
However, once we know the exactly initial conditions and the Markov process, the theory is in fact a realistic interpretation of quantum mechanics.
Moreover, to know the motion of the particles at any moment, you have to know what the Markov process is.