Stochastic deformation of integrable dynamical systems and random time symmetry.

We present a deformation of a class of elementary classical integrable systems using stochastic diffusion processes. This deformation applies to the solution of the associated classical Newtonian, Hamiltonian, Lagrangian, and variational problems and to the Hamilton-Jacobi method of characteristics. The underlying stochastic action functionals involve dual random times, whose expectations are connected to the new variables of the system after a canonical transformation. [ABSTRACT FROM AUTHOR]