  We study a connection between the algebraic probability and classical
stochastic processes described by master equations. Introducing a definition of
a state which has not been used for quantum cases, the classical stochastic
processes can be reformulated in terms of the algebraic probability. This
reformulation immediately gives the Doi-Peliti formalism, which has been
frequently used in nonequilibrium physics. As an application of the
reformulation, we give a derivation of basic equations for counting statistics,
which plays an important role in nonequilibrium physics.
