On Adjoint Additive Processes

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 $\delta_{\psi,t}$.