Markov Chain

Markov chain is a stochastic process ⚠ $x_{i}$ satisfying

⚠ $p (x_{i} ∣ x_{i - 1}, \dots, x_{1}) = T (x_{i}, x_{i - 1}) .$

The conditional probability of being in the state ⚠ $x_{i}$ after states depends only on the current state ⚠ $x_{i - 1}$ and is defined by the transition matrix ⚠ $T$ . This property is called Markov property. If ⚠ $T (x_{i} ∣ x_{j}) = T (x_{j} ∣ x_{i})$ the chain is called homogeneous. See also http://en.wikipedia.org/wiki/Markov_chain.