  Matrix-valued stochastic processes have been of significant importance in
areas such as physics, engineering and mathematical finance. One of the first
models studied has been the so-called Wishart process, which is described as
the solution of a stochastic differential equation in the space of matrices. In
this paper we analyze natural extensions of this model, and prove the existence
and uniqueness of the solution. We do this by carrying out a Picard iteration
technique in the space of symmetric matrices. This approach takes into account
the operator character of the matrices, which helps to corroborate how the
Lipchitz conditions also arise naturally in this context.
