  We define an operator which extends classical differentiation from smooth
deterministic functions to certain stochastic processes. Based on this
operator, we define a procedure which associates a stochastic analog to
standard differential operators and ordinary differential equations. We call
this procedure stochastic embedding. By embedding lagrangian systems, we obtain
a stochastic Euler-Lagrange equation which, in the case of natural lagrangian
systems, is called the embedded Newton equation. This equation contains the
stochastic Newton equation introduced by Nelson in his dynamical theory of
brownian diffusions. Finally, we consider a diffusion with a gradient drift, a
constant diffusion coefficient and having a probability density function. We
prove that a necessary condition for this diffusion to solve the embedded
Newton equation is that its density be the square of the modulus of a wave
function solution of a linear Schr\"{o}dinger equation.
