  The path integral for classical statistical dynamics is used to determine the
properties of one-dimensional Darcy flow through a porous medium with a
correlated stochastic permeability for several spatial correlation lengths.
Pressure statistics are obtained from the numerical evaluation of the path
integral by using the Markov chain Monte Carlo method. Comparisons between
these pressure distributions and those calculated from the classic
finite-volume method for the corresponding stochastic differential equation
show excellent agreement for Dirichlet and Neumann boundary conditions. The
evaluation of the variance of the pressure based on a continuum description of
the medium provides an estimate of the effects of discretization. Log-normal
and Gaussian fits to the pressure distributions as a function of position
within the porous medium are discussed in relation to the spatial extent of the
correlations of the permeability fluctuations.
