Bryc's random fields: the existence and distributions analysis

2005/07/14 by Wojciech Matysiak, Matysiak, Wojciech, Paweł J. Szabłowski +1
Mathematics · #60G10 #60G12 #60J05 #FOS: Mathematics #Probability (math.PR) #Probability and Statistical Research #math.PR #msc:60G10 #msc:60G12 #msc:60J05

paper · pdf · doi:10.48550/arxiv.math/0507296

11 pages

openalex publication_date 2005/07/14 · arxiv created 2005/07/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine problem of existence of stationary random fields with linear regressions and quadratic conditional variances, introduced by Bryc in "Stationary random fields with linear regressions" (Annals of Probability 29, No. 1, 504-519). Distributions of the fields are identified and almost complete description of the possible sets of parameters defining the first two conditional moments is given. This note almost solves Bryc's problem concerning fields undetermined by moments - the only remaining set of parameters for which the existence of Bryc's fields is unclear has Lebesgue measure zero.

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