Musielak-Orlicz spaces and prediction problems

• Autorzy: Kazimierz Urbanik
• Języki publikacji: EN

Abstrakty

EN

By a harmonizable sequence of random variables we mean the sequence of Fourier coefficients of a random measure M:
$Xₙ(M) = ∫_{0}^{1} e^{2πnis}M(ds)$ (n = 0,±1,...)
The paper deals with prediction problems for sequences {Xₙ(M)} for isotropic and atomless random measures M. The crucial result asserts that the space of all complex-valued M-integrable functions on the unit interval is a Musielak-Orlicz space. Hence it follows that the problem for {Xₙ(M)} (n = 0,±1,...) to be deterministic is in fact an extremal problem of Szegö's type for Musielak-Orlicz spaces in question. This leads to a characterization of deterministic sequences {Xₙ(M)} (n = 0,±1,...) in terms of random measures M.

Kategorie tematyczne

• 60G25: Prediction theory
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 60G57: Random measures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2004
• Tom: 64
• Numer: 1
• Strony: 207-219

Daty

wydano

2004

Twórcy

autor

Kazimierz Urbanik

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa 10, Poland

Identyfikatory

DOI

10.4064/bc64-0-16