Lecture notes on Markov chains

نویسنده

Olivier Lévêque

چکیده

If moreover P(Xn+1 = j|Xn = i) = pij is independent of n, then X is said to be a timehomogeneous Markov chain. We will focus on such chains during the course. Terminology. * The possible values taken by the random variables Xn are called the states of the chain. S is called the state space. * The chain is said to be finite-state if the set S is finite (S = {0, . . . , N}, typically). * P = (pij)i,j∈S is called the transition matrix of the chain. Properties of the transition matrix. * pij ≥ 0, ∀i, j ∈ S. * ∑ j∈S pij = 1, ∀i ∈ S. It is always possible to represent a time-homogeneous Markov chain by a transition graph.

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