The bi-Poisson process: A quadratic harness

• 成果类型: Article
• 署名作者: Bryc, Wlodzimierz; Matysiak, Wojciech; Wesolowski, Jacek
• 署名单位: University System of Ohio; University of Cincinnati; Warsaw University of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117907000000268
• 发表日期: 2008
• 页码: 623-646
• 关键词: wilson polynomials

摘要

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.