  The derivation of path integrals is reconsidered. It is shown that the
expression for the discretized action is not unique, and the path integration
domain can be deformed so that at least Gaussian path integrals become
probabillistic. This leads to a practical algorithm of sign-problem-free Monte
Carlo sampling from the Gaussian path integrals. Moreover, the dynamical
influence of Gaussian quantum system (the bath) on any other quantum system can
be exactly represented as interaction with classical non-Markovian noise. We
discuss the relation of these findings to the Bell's theorem and the Feynman's
conjecture on the exponential complexity of the classical simulation of quantum
systems. In Feynman's path integral we have quasiprobability distributions for
trajectories, and in analitycally continued path integrals we have probability
distributions for quasitrajectories.
