4. Markov chain applications
The applications of Markov chains are extremely varied, and it is of course out of the question to mention them all (see, for example, and ). We will therefore restrict ourselves to a few examples to highlight widely-used algorithmic procedures.
4.1 Hastings-Metropolis algorithm
Let E be a countable space. We wish to find a procedure for simulating a random variable with a law λ that can always be assumed to be strictly positive, this law being known to within one multiplicative constant, for example a Gibbs measure of the form
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