  We investigate lattice simulations of scalar and nonabelian gauge fields in
Minkowski space-time. For SU(2) gauge-theory expectation values of link
variables in 3+1 dimensions are constructed by a stochastic process in an
additional (5th) ``Langevin-time''. A sufficiently small Langevin step size and
the use of a tilted real-time contour leads to converging results in general.
All fixed point solutions are shown to fulfil the infinite hierarchy of
Dyson-Schwinger identities, however, they are not unique without further
constraints. For the nonabelian gauge theory the thermal equilibrium fixed
point is only approached at intermediate Langevin-times. It becomes more stable
if the complex time path is deformed towards Euclidean space-time. We analyze
this behavior further using the real-time evolution of a quantum anharmonic
oscillator, which is alternatively solved by diagonalizing its Hamiltonian.
Without further optimization stochastic quantization can give accurate
descriptions if the real-time extend of the lattice is small on the scale of
the inverse temperature.
