BI-POISSON PROCESS

2004/04/13 by Wlodzimierz Bryc, WŁODZIMIERZ BRYC, Jacek Wesolowski +1 · 3 citations
Decision Sciences · Mathematics · #Point processes and geometric inequalities #Probability and Risk Models #Random Matrices and Applications #math.PR #msc:60J25

paper · pdf · doi:10.1142/s0219025707002737

published as Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 10, No. 2 (2007) 277-291 · 12 pages, 2 figures

arxiv created 2004/04/13 · openalex publication_date 2007/06/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Bi-Poisson processes are defined as a two-parameter family of processes with linear regressions and linear conditional variances. We give conditions for the existence and uniqueness of such processes. We point out that one-dimensional distributions of the bi-Poisson process are closed under a generalized free convolution introduced by Bożejko and Speicher. 7 .

Citations

• Free martingale polynomials

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