TITLE: (Stochastic) matrix for which a stochastic matrix logarithm exists?
QUESTION [5 upvotes]: I think this is basically the inverse question of Matrices whose exponential is stochastic. 
i.e. what are sufficient conditions on the matrix representation of an evolution operator of a (finite) discrete Markov chain for it to be embeddable in a continuous Markov chain?
I've found some old paper that may answer this (something about embeddability criteria) but I can't access it as it published in a closed-access journal.
I hope this is a sane question.

REPLY [5 votes]: Steve Hunstman's link above is good:
See the part leading up to Theorem 9 for something relevant to applications:

The main application of the following
  theorem may be to establish that
  certain Markov matrices arising in
  applications are not embeddable, and
  hence either that the entries are not
  numerically accurate or that the
  underlying process is not autonomous.
  The theorem is a quantitative
  strengthening of Lemma 8. It is of
  limited value except when n is fairly
  small, but this is often the case in
  applications.

Also the part on regularization for best compromises when matrices are not embeddable.