Let be the total number of possible states. The -matrix
and
the -vector
consisting of the individual probabilities
determine the statistical properties of the Markov chain uniquely.
A Markov chain is reversible if
(3.1) |
The elements of the matrix
are not uniquely defined
by the reversibility conditions.
For a given distribution density
there are
many reversible transition matrices.
``Asymmetrical rule'' (N. Metropolis):