Transition-rate matrix
Matrix describing continuous-time Markov chains / From Wikipedia, the free encyclopedia
In probability theory, a transition-rate matrix (also known as a Q-matrix,[1] intensity matrix,[2] or infinitesimal generator matrix[3]) is an array of numbers describing the instantaneous rate at which a continuous-time Markov chain transitions between states.
In a transition-rate matrix (sometimes written
[4]), element
(for
) denotes the rate departing from
and arriving in state
. The rates
, and the diagonal elements
are defined such that
,
and therefore the rows of the matrix sum to zero.
Up to a global sign, a large class of examples of such matrices is provided by the Laplacian of a directed, weighted graph. The vertices of the graph correspond to the Markov chain's states.