OPERATOR FRACTIONAL BROWNIAN MOTION AS LIMIT OF POLYGONAL LINES PROCESSES IN HILBERT SPACE

DOI10.1142/S0219493711003152zbMath1228.60045MaRDI QIDQ3083429

Charles Suquet, Alfredas Račkauskas

Publication date: 21 March 2011

Published in: Stochastics and Dynamics (Search for Journal in Brave)

zbMATH Keywords

functional central limit theoremHilbert spacefractional Brownian motionlong memorylinear processes

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Functional limit theorems; invariance principles (60F17) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items

The central limit theorem for a sequence of random processes with space-varying long memory ⋮ Operator self-similar processes and functional central limit theorems ⋮ Tempered functional time series ⋮ Limit theorems in the context of multivariate long-range dependence ⋮ Weakly stationary stochastic processes valued in a separable Hilbert space: Gramian-cramér representations and applications ⋮ On convex hull of \(d\)-dimensional fractional Brownian motion ⋮ On the convex hull and winding number of self-similar processes ⋮ Limit theorems for Hilbert space-valued linear processes under long range dependence ⋮ Asymptotic normality of sums of Hilbert space valued random elements ⋮ A moment-based notion of time dependence for functional time series ⋮ Spectral analysis of multifractional LRD functional time series

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On limit theorems for Banach-space-valued linear processes
• Operator self similar stochastic processes in \(R^ n\).
• Weak convergence of multivariate fractional processes
• The conditional central limit theorem in Hilbert spaces.
• FRACTIONAL BROWNIAN MOTION AND STOCHASTIC EQUATIONS IN HILBERT SPACES
• Asymptotic inference results for multivariate long‐memory processes
• Long Range Dependence
• Fractional Brownian Motions, Fractional Noises and Applications