On Adjoint Additive Processes

Abstract

Starting with an additive process $(Y_t{)}_{t\ge 0}$, it is in certain cases possible to construct an adjoint process $(X_t{)}_{t\ge 0}$ which is itself additive. Moreover, assuming that the transition densities of $(Y_t{)}_{t\ge 0}$ are controlled by a natural pair of metrics ${\mathrm{d}}_{\psi ,t}$ and ${\delta }_{\psi ,t}$, we can prove that the transition densities of $(X_t{)}_{t\ge 0}$ are controlled by the metrics ${\delta }_{\psi ,1/t}$ replacing ${\mathrm{d}}_{\psi ,t}$ and ${\mathrm{d}}_{\psi ,1/t}$ replacing ${\delta }_{\psi ,t}$.

22 pages