Multiple Wiener-Itô integrals. With applications to limit theorems

DOI10.1007/978-3-319-02642-8zbMath1301.60004OpenAlexW4234924739MaRDI QIDQ388754

Péter Major

Publication date: 6 January 2014

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-02642-8

zbMATH Keywords

non-central limit theoremstationary Gaussian fieldsmultiple Wiener-Itō integralsFeynman's diagramsrandom spectral measuresWick polynomials

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Central limit and other weak theorems (60F05) Stochastic integrals (60H05) Self-similar stochastic processes (60G18) Research exposition (monographs, survey articles) pertaining to probability theory (60-02)

Related Items (26)

A central limit theorem for the Euler integral of a Gaussian random field ⋮ Spatiotemporal covariance functions for Laplacian ARMA fields in higher dimensions ⋮ Asymptotic analysis of higher-order scattering transform of Gaussian processes ⋮ Determinantal structures in the O'Connell-Yor directed random polymer model ⋮ Non-Gaussian limit of a tracer motion in an incompressible flow ⋮ Multiple stochastic integrals with dependent integrators ⋮ Stationarity and second-order properties of a scalar-valued nonlinear time series with Gaussian residuals ⋮ Non-central limit theorems for quadratic functionals of Hermite-driven long memory moving average processes ⋮ Evolutionary transfer functions of bilinear processes with time-varying coefficients ⋮ Limit theorems in the context of multivariate long-range dependence ⋮ One Limit Theorem for Branching Random Walks ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Solving SPDEs driven by colored noise: A chaos approach ⋮ Representations of hermite processes using local time of intersecting stationary stable regenerative sets ⋮ Sensitivity of the Hermite rank ⋮ How the instability of ranks under long memory affects large-sample inference ⋮ On Weak Convergence in Dynamical Systems to Self-Similar Processes with Spectral Representation ⋮ Weak convergence of functionals of stationary long memory processes to Rosenblatt-type distributions ⋮ Goodness-of-fit testing under long memory ⋮ Functional limit theorems for power series with rapid decay of moving averages of Hermite processes ⋮ Towards three-dimensional conformal probability ⋮ Almost sure convergence on chaoses ⋮ Weak convergence of weighted additive functionals of long-range dependent fields ⋮ Unnamed Item ⋮ A coupled KPZ equation, its two types of approximations and existence of global solutions

This page was built for publication: Multiple Wiener-Itô integrals. With applications to limit theorems