Bridges of quadratic harnesses

Abstract

Quadratic harnesses are typically non-homogeneous Markov processes with time-dependent state space. Motivated by a question raised in Émery and Yor (2004) we give explicit formulas for bridges of such processes. Using an appropriately defined f transformation we show that all bridges of a given quadratic harness can be transformed into other standard quadratic harnesses. Conversely, each such bridge is anf-transformation of a standard quadratic harness. We describe quadratic harnesses that correspond to bridges of some Lévy processes. We determine all quadratic harnesses that may arise from stitching together a pair of q-Meixner processes.