Bridges of quadratic harnesses

Włodek Bryc (University of Cincinnati)
Jacek Wesołowski (Warsaw University of Technology)

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.

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Pages: 1-25

Publication Date: December 21, 2012

DOI: 10.1214/EJP.v17-1866

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