  A permanental vector is a generalization of a vector with components that are
squares of the components of a Gaussian vector, in the sense that the matrix
that appears in the Laplace transform of the vector of Gaussian squares is not
required to be either symmetric or positive definite. In addition the power of
the determinant in the Laplace transform of the vector of Gaussian squares,
which is -1/2, is allowed to be any number less than zero.
  It was not at all clear what vectors are permanental vectors. In this paper
we characterize all permanental vectors in $R^{3}_{+}$ and give applications to
permanental vectors in $R^{n}_{+}$ and to the study of permanental processes.
