We use generalized beta integrals to construct examples of Markov processes with linear regressions, and quadratic second conditional moments.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-4, author = {W\l odek Bryc}, title = {Quadratic harnesses from generalized beta integrals}, journal = {Banach Center Publications}, volume = {95}, year = {2011}, pages = {67-79}, zbl = {1255.60123}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-4} }
Włodek Bryc. Quadratic harnesses from generalized beta integrals. Banach Center Publications, Tome 95 (2011) pp. 67-79. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-4/