Wilson's 6-j laws and stitched Markov processes
arXiv:1109.2539 · doi:10.4213/tvp4622
Abstract
We show how to insert time into the parameters of the Wilson's 6-j laws to construct discrete Markov chains with these laws. By a quadratic transformation we convert them into Markov processes with linear regressions and quadratic conditional variances. Further conversion into the "standard form" gives "quadratic harnesses" with "classical" value of parameter gamma. A random-parameter-representation of the original Markov chain allows us to stitch together two copies of the process, extending time domain of the quadratic harness from (0,1) to all t>0.
28 pages, 1 figure