diag(Q) is the diagonal matrix formed by selecting the main diagonal from the matrix Q and setting all other elements to zero. To find the stationary probability distribution vector, we must next find such that with being a row vector, such that all elements in are greater than 0 and = 1. From this, may be found as (S may be periodic, even if Q is not. Once is found, it must be normalized to a unit vector.) Another discrete-time process that may be derived from a continuous-time Markov chain is a δ-skeleton—the (discrete-time) Markov chain formed by observing X(t) at intervals of δ units of time. The random variables X(0), X(δ), X(2δ), ... give the sequence of states visited by the δ-skeleton. See also Kolmogorov equations (Markov jump process) Notes References Leo Breiman (1992) [1968] Probability. Original edition published by Addison-Wesley; reprinted by Society for Industrial and Applied Mathematics . (See Chapter 7) J. L. Doob (1953) Stochastic Processes. New York: John Wiley and Sons . A. A. Markov (1971). "Extension of the limit theorems of probability theory to a sum of variables connected in a chain". reprinted in Appendix B of: R. Howard. Dynamic Probabilistic Systems, volume 1: Markov Chains. John Wiley and Sons. S. P. Meyn and R. L. Tweedie (1993) Markov Chains and Stochastic Stability. London: Springer-Verlag . online: MCSS . Second edition to appear, Cambridge University Press, 2009. Classical text. cf Chapter 6 Finite Markov Chains pp. 384ff. John G. Kemeny & J. Laurie Snell (1960) Finite Markov Chains, D. van Nostrand Company E. Nummelin. "General irreducible Markov chains and non-negative operators". Cambridge University Press, 1984, 2004. Seneta, E. Non-negative matrices and Markov chains. 2nd rev. ed., 1981, XVI, 288 p., Softcover Springer Series in Statistics. (Originally published by Allen & Unwin Ltd., London, 1973) Markov processes