Stochastic simulations: continuous approximation of quantum noise

The stochastic simulations of quantum evolution are introduced, alternatively, to the Ito-stochastic simulations, for the normal, symmetrical and antinormal ordering in the double-dimensional phase space. The nonclassical effects in the linearized parametric amplifier can be very well simulated in contrast to the collapses-revivals effect in a nonlinear version, which is stimulated by the discreteness of light. The reason is that the stochastic simulations use the continuous variables, whereas the quantum noise in nonlinear systems cannot generally be treated continuously.