The nu(3) vibrational mode of (CO2)-C-13, trapped in a rare gas matrix, is excited by a laser pulse near 2300 cm(-1). Emission is then observed in the 16 mum region and assigned to three transitions: namely, 3nu(2)(1)-2nu(2)(0), 3nu(2)(1)-2nu(2)(2), and 2nu(2)(0)-nu(2)(1), which are all observed in neon and for the two sites in argon. 3nu(2)(1)-2nu(2)(2) is missing in krypton. In xenon the emission, much weaker and longer (ms range), cannot be frequency resolved and behaves like spontaneous emission. In the other cases, all the recorded signals exhibit the characteristics of vibrational stimulated emission (VSE). The temporal profile of VSE is different for the three transitions and highly depends on the matrix material (1-100 mus). The relative intensities of the different VSE transitions depend on the matrix and on the energy of the exciting pulse. These results are interpreted using a kinetic model which takes into account absorption, spontaneous and stimulated emission, and nonradiative transfers between the involved vibrational levels. The model provides numerical simulations of the emissions, which are adjusted to experimental features (time behavior and relative intensities). Orders of magnitude values are thus extracted for the transfer rates and compared to literature values.