(D+1)-Dimensional Formulation for D-Dimensional Constrained Systems
  D-dimensional constrained systems are studied with stochastic Lagrangian and\break Hamiltonian. It is shown that stochastic consistency conditions are second class constraints and Lagrange multiplier fields can be determined in (D+1)-dimensional canonical formulation. The Langevin equations for the constrained system are obtained as Hamilton's equations of motion where conjugate momenta play a part of noise fields. 
R. Mochizuki and K. Yoshida