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

Algebraic probability, classical stochastic processes, and counting statistics