Double stochastic integrals, random quadratic forms and random series in Orlicz spaces

DOI10.1214/aop/1176992082zbMath0622.60054OpenAlexW2078018789MaRDI QIDQ1091038

Stanislaw Kwapien, Wojbor A. Woyczyński

Publication date: 1987

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176992082

zbMATH Keywords

Orlicz spacerandom quadratic formdouble stochastic integralssymmetric and stationary increments

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Stochastic integrals (60H05) Probability theory on linear topological spaces (60B11) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items

Necessary and sufficient conditions for the strong law of large numbers for \(U\)-statistics. ⋮ Almost sure convergence of smoothing \(D^ m\)-splines of noisy data ⋮ Bounded laws of the iterated logarithm for quadratic forms in Gaussian random variables ⋮ Multiple stable integrals of Banach-valued functions ⋮ Sample path properties of stochastic processes represented as multiple stable integrals ⋮ Gaussian chaos laws on Banach function spaces ⋮ Absolute continuity of joint laws of multiple stable stochastic integrals ⋮ Large violation of Bell inequalities with low entanglement ⋮ Symmetric infinitely divisible processes with sample paths in Orlicz spaces and absolute continuity of infinitely divisible processes ⋮ Resampling \(U\)-statistics using \(p\)-stable laws ⋮ Multiple integration with respect to Poisson and Lévy processes ⋮ Hyperbolic asymptotics in Burgers' turbulence and extremal processes ⋮ Stochastic integration with respect to canonical \(\alpha\)-stable cylindrical Lévy processes ⋮ Functional limit theorems for random quadratic forms ⋮ Weak invariance principles for weighted \(U\)-statistics