On integrability of quadratic harnesses

• Autorzy: Bryc W.
• Języki publikacji: EN

Abstrakty

EN

We investigate integrability properties of processes with linear regressions and quadratic conditional variances. We establish the right order of dependence of which moments are finite on the parameter (…) defined below, raising the question of determining the optimal constant.

Słowa kluczowe

EN

integrability; polynomial regression; quadratic harnesses

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2012
• Tom: Vol. 45, nr 2
• Strony: 275--282
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Bryc W.

• Department Of Mathematical Sciences University Of Cincinnati Po Box 210025 Cincinnati, Oh 45221-0025, USA,

Bibliografia

• [1] W.Bryc, J.Wesołowski, Askey–Wilson polynomials, quadratic harnesses and martingales Ann.Probab.38(3)(2010),1221 .1262.
• [2] W.Bryc, Stationary random fields with linear regressions Ann.Probab.29 (2001), 504 .519.
• [3] W.Bryc, W.Matysiak, J.Wesołowski, Quadratic harnesses, q-commutations, and orthogonal martingale polynomials Trans.Amer.Math.Soc.359 (2007),5449 .5483. arxiv.org/abs/math.PR/0504194.
• [4] W.Bryc, A.Plucińska, A characterization of infinite Gaussian sequences by conditional moments Sankhya A 47 (1985),166 .173.
• [5] M.Jamiońkowska, Bi-Pascal process – definition and properties Master ’s thesis, Warsaw University of Technology,(in Polish),2009.
• [6] A.Plucińska, On a stochastic process determined by the conditional expectation and the conditional variance Stochastics 10 (1983),115 .129.
• [7] P.J.Szabłowski, Can the first two conditional moments identify a mean square differentiable process?,Comput.Math.Appl.18(4)(1989),329 .348.
• [8] P.J.Szabłowski, Some remarks on two-dimensional elliptically contoured measures with second moments Demonstratio Math.19(4)(1987),915 .929.
• [9] J.Wesołowski, Stochastic processes with linear conditional expectation and quadratic conditional variance Probab.Math.Statist.14 (1993),33 .44.