Variable-order Markov model: Difference between revisions

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==Definition==

Let <math>A</math> be a state space (finite [[alphabet]]) of size <nowikimath>|A|</nowikimath>.

Consider a sequence with the [[Markov property]] <math>x_1^{n}=x_1x_2\dots x_n</math> of <math>n</math> realizations of [[random variable]]s, where <math> x_i\in A</math> is the state (symbol) at position <math>i</math> 1≤<math>i</math>≤<math>n</math>, and the concatenation of states <math>x_i</math> and <math>x_{i+1}</math> is denoted by <math>x_ix_{i+1}</math>.