  The stochastic variational method is applied to particle systems and
continuum mediums. As the brief review of this method, we first discuss the
application to particle Lagrangians and derive a diffusion-type equation and
the Schr\"{o}dinger equation with the minimum gauge coupling. We further extend
the application of the stochastic variational method to Lagrangians of
continuum mediums and show that the Navier-Stokes, Gross-Pitaevskii and
generalized diffusion equations are derived. The correction term for the
Navier-Stokes equation is also obtained in this method. We discuss the meaning
of this correction by comparing with the diffusion equation.
