  The time evolution of probability densities for solutions to stochastic
differential equations (SDEs) without delay is usually described by
Fokker-Planck equations, which require the adjoint of the infinitesimal
generator for the solutions. However, Fokker-Planck equations do not exist for
stochastic delay differential equations (SDDEs) because the solutions to SDDEs
are not Markov processes and have no corresponding infinitesimal generators. In
this paper, we address the open question of finding the governing equations for
probability densities of SDDEs with discrete time delays. The governing
equation is given in a simple form that facilitates theoretical analysis and
numerical computation. An illustrative example is presented to verify the
proposed governing equations.
