  A non-critical branching immigration superprocess with dependent spatial
motion is constructed and characterized as the solution of a stochastic
equation driven by a time-space white noise and an orthogonal martingale
measure. A representation of its conditional log-Laplace functionals is
established, which gives the uniqueness of the solution and hence its Markov
property. Some properties of the superprocess including an ergodic theorem are
also obtained.
