Résumé
In this article, we find the transition densities of the basic affine jump-diffusion (BAJD), which has been introduced by Duffie and Garleanu as an extension of the CIR model with jumps. We prove the positive Harris recurrence and exponential ergodicity of the BAJD. Furthermore, we prove that the unique invariant probability measure of the BAJD is absolutely continuous with respect to the Lebesgue measure and we also derive a closed-form formula for the density function of pi.