Abstract: Starting with an additive process \((Y_t)_{t\geq0}\), it is in certain cases possible to construct an adjoint process \((X_t)_{t\geq0}\) which is itself additive. Moreover, assuming that the transition densities of \((Y_t)_{t\geq0}\) are controlled by a natural pair of metrics \(\mathrm{d}_{\psi,t}\) and \(\delta_{\psi,t}\), we can prove that the transition densities of \((X_t)_{t\geq0}\) are controlled by the metrics \(\delta_{\psi,1/t}\) replacing \(\mathrm{d}_{\psi,t}\) and \(\mathrm{d}_{\psi,1/t}\) replacing \(\delta_{\psi,t}\).

2010 AMS Mathematics Subject Classification: Primary 60J30, 60J35, 60E07, 60E10, 47D03, 47D06; Secondary XXXX.

Keywords and phrases: additive processes, L\'evy processes, adjoint densities, transition functions, metric measure spaces.