Associated with the ground state of a quantum system, there is a unique stochastic process which, in general, has diffusion and jumping components. This is illustrated in two exact models. The drift and the jumping kernel of the ground-state process may be obtained directly without solving the Schrodinger equation. A method is proposed to extract expectation values and Euclidian correlation functions from a numerical simulation of the process. The method applies equally well to boson and fermion systems, without the sign problem.

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We use an off-lattice discretization of fractional Brownian motion and a Metropolis Algorithm to determine the asymptotic scaling of this discretized fractional Brownian motion under the influence of an 1 arXiv:1501.02326v1 [physics.comp-ph]