Bryc, Włodek; Wesołowski, Jacek Bridges of quadratic harnesses. (English) Zbl 1291.60151 Electron. J. Probab. 17, Paper No. 105, 25 p. (2012). 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. Cited in 4 Documents MSC: 60J25 Continuous-time Markov processes on general state spaces 60G51 Processes with independent increments; Lévy processes Keywords:bridges; harnesses; Lévy-Meixner processes; quadratic conditional variances Citations:Zbl 1074.60054 PDFBibTeX XMLCite \textit{W. Bryc} and \textit{J. Wesołowski}, Electron. J. Probab. 17, Paper No. 105, 25 p. (2012; Zbl 1291.60151) Full Text: DOI