  Open, dissipative systems subject to a random force are directly quantized.
The starting point is the effective action derived using the method of
Parisi-Sourlas. Since the effective action is second-order, the method of
Ostrogradsky was used to quantize the system canonically. In the case of the
harmonic oscillator, the relevant Green function can be computed exactly. In
the general case, a perturbation expansion, involving time-dependent (memory)
terms, can be defined.
