  Several types of stochastic equations are important in thermodynamics,
chemistry, evolutionary biology, population dynamics and quantitative social
science. For systems with pair interactions four different types of equations
are derived, starting from a master equation for the state space: First,
general mean value and (co)variance equations. Second, Boltzmann-like
equations. Third, a master equation for the configuration space allowing
transition rates which depend on the occupation numbers of the states. Fourth,
a Fokker-Planck equation and a ``Boltzmann-Fokker-Planck equation''. The
interrelations of these equations and the conditions for their validity are
worked out clearly. A procedure for a selfconsistent solution of the nonlinear
equations is proposed. Generalizations to interactions between an arbitrary
number of systems are discussed.
