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March 2008 The bi-Poisson process: A quadratic harness
Włodzimierz Bryc, Wojciech Matysiak, Jacek Wesołowski
Ann. Probab. 36(2): 623-646 (March 2008). DOI: 10.1214/009117907000000268

Abstract

This paper is a continuation of our previous research on quadratic harnesses, that is, processes with linear regressions and quadratic conditional variances. Our main result is a construction of a Markov process from given orthogonal and martingale polynomials. The construction uses a two-parameter extension of the Al-Salam–Chihara polynomials and a relation between these polynomials for different values of parameters.

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Włodzimierz Bryc. Wojciech Matysiak. Jacek Wesołowski. "The bi-Poisson process: A quadratic harness." Ann. Probab. 36 (2) 623 - 646, March 2008. https://doi.org/10.1214/009117907000000268

Information

Published: March 2008
First available in Project Euclid: 29 February 2008

zbMATH: 1137.60036
MathSciNet: MR2393992
Digital Object Identifier: 10.1214/009117907000000268

Subjects:
Primary: 60J25

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 2 • March 2008
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