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Bridges of quadratic harnesses. (English) Zbl 1291.60151

Summary: Quadratic harnesses are typically non-homogeneous Markov processes with time-dependent state space. Motivated by a question raised in [M. Émery and M. Yor, Publ. Res. Inst. Math. Sci. 40, No. 3, 669–688 (2004; Zbl 1074.60054)] 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 an \(f\)-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.

MSC:

60J25 Continuous-time Markov processes on general state spaces
60G51 Processes with independent increments; Lévy processes

Citations:

Zbl 1074.60054
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