On the convergence rate of strictly sub-Gaussian random series in the norm of the space \(L_ p\). (English. Ukrainian original) Zbl 0840.60036

Kozachenko, Yu. V.; Trigub, S. G.

Theory Probab. Math. Stat. 48, 35-45 (1994); translation from Teor. Jmovirn. Mat. Stat. 48, 51-66 (1993).

Summary: Random fields of the form \(S(t) = \sum^\infty_{k = 1} \xi_k \varphi_k (t)\), \(t \in [0,T]\), where \(\xi_k\) are jointly strictly sub-Gaussian random variables and \(\{\varphi_k (t), t \in [0,T], k \geq 1\}\) is a system of bounded measurable functions are studied. Conditions for convergence and estimates of the convergence rate of these series in the norm of the space \(L_p ([0,T])\) are established.

MSC:

60G15	Gaussian processes
60F25	\(L^p\)-limit theorems
46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords:

conditions for convergence; random fields; sub-Gaussian random variables; estimates of the convergence rate