matrices - (Stochastic) matrix for which a stochastic matrix logarithm exists?

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.