Matrix of transition probabilities
The matrices of a Markov chain with discrete time or a regular Markov chain with continuous time satisfy the following conditions for any and :
i.e. they are stochastic matrices (cf. Stochastic matrix), while for irregular chains
such matrices are called sub-stochastic.
By virtue of the basic (Chapman–Kolmogorov) property of a homogeneous Markov chain,
the family of matrices forms a multiplicative semi-group; if the time is discrete, this semi-group is uniquely determined by .
|[a1]||K.L. Chung, "Elementary probability theory with stochastic processes" , Springer (1974)|
Matrix of transition probabilities. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Matrix_of_transition_probabilities&oldid=47796