Oscillatory fractional Brownian motion

DOI10.1007/s10440-013-9798-3zbMath1311.60043arXiv1201.5084OpenAlexW2065160605MaRDI QIDQ385587

Anna Talarczyk, Tomasz Bojdecki, Louis G. Gorostiza

Publication date: 2 December 2013

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.5084

zbMATH Keywords

branching processesGaussian processeslimit theoremhierarchical random walkultrametric spacesoscillatory fractional Brownian motionoscillatory sub-fractional Brownian motionsemi-selfsimilar processes

Mathematics Subject Classification ID

Gaussian processes (60G15) Fractional processes, including fractional Brownian motion (60G22) Self-similar stochastic processes (60G18) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Functional limit theorems; invariance principles (60F17)

Related Items (4)

Modified fractional Cauchy problem in a complex domain ⋮ Oscillatory fractional Brownian motion ⋮ Transience and recurrence of random walks on percolation clusters in an ultrametric space ⋮ Random systems in ultrametric spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Oscillatory fractional Brownian motion
• A complement to Gladyshev's theorem
• Particle picture interpretation of some Gaussian processes related to fractional Brownian motion
• Number variance for hierarchical random walks and related fluctuations
• Particle systems with quasi-homogeneous initial states and their occupation time fluctuations
• Fractional Brownian density process and its self-intersection local time of order \(k\)
• A series expansion of fractional Brownian motion
• Weak convergence towards two independent Gaussian processes from a unique Poisson process
• A decomposition of the bifractional Brownian motion and some applications
• Semi-selfsimilar processes
• Sub-fractional Brownian motion and its relation to occupation times
• Degrees of transience and recurrence and hierarchical random walks
• Occupation time fluctuations of weakly degenerate branching systems
• Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems
• Self-similar stable processes arising from high-density limits of occupation times of particle systems
• On the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions
• Limit theorems for occupation time fluctuations of branching systems. I: long-range dependence
• Limit theorems for occupation time fluctuations of branching systems. II: Critical and large dimensions
• A New Limit Theorem for Stochastic Processes with Gaussian Increments
• Some properties of the sub-fractional Brownian motion
• Fourier Integrals and Metric Geometry
• Occupation time fluctuations in branching systems

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