  Using a matrix approach, we define the free Jacobi process as the limit of
the complex Jacobi matrix process. The we derive a free SDE which is analogous
to its classical counterpart. To proceed, we prove that fro suitable parameters
the process remains injective if it is initially injective and then use the
polar decomposition. In the stationnary case, this will be easily deduced from
the explicit expression of the spectral measure. In the general setting we
derive a recurrence formula for the moments. Moreover, a p. d. e. for the
Cauchy transform of the law is given.

Probability