Particle picture interpretation of some Gaussian processes related to fractional Brownian motion

DOI10.1016/j.spa.2012.03.004zbMath1242.60036arXiv1108.2745OpenAlexW2130488824MaRDI QIDQ424526

Tomasz Bojdecki, Anna Talarczyk

Publication date: 1 June 2012

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.2745

zbMATH Keywords

fractional Brownian motionparticle systemsub-fractional Brownian motiondensity processnegative sub-fractional Brownian motionoccupation time fluctuation limit

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Fractional processes, including fractional Brownian motion (60G22) Generalized stochastic processes (60G20) Stable stochastic processes (60G52) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (6)

Unnamed Item ⋮ Oscillatory fractional Brownian motion ⋮ From intersection local time to the Rosenblatt process ⋮ Self-similar stochastic processes with stationary increments as limits of particle systems ⋮ A note on Riemann-Liouville processes ⋮ A CLASS OF FRACTIONAL BROWNIAN FIELDS FROM BRANCHING SYSTEMS AND THEIR REGULARITY PROPERTIES

Cites Work

• Particle systems with quasi-homogeneous initial states and their occupation time fluctuations
• A series expansion of fractional Brownian motion
• Occupation time fluctuations of an infinite-variance branching system in large dimensions
• Weak convergence towards two independent Gaussian processes from a unique Poisson process
• Erratum to ``Number variance from a probabilistic perspective, infinite systems of independent Brownian motions and symmetric \(\alpha\)-stable processes
• High density limit theorems for infinite systems of unscaled branching Brownian motions
• Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motions
• Large deviations for the occupation time functional of a Poisson system of independent Brownian particles
• Multiple scale analysis of clusters in spatial branching models
• Sub-fractional Brownian motion and its relation to occupation times
• Occupation time fluctuations of weakly degenerate branching systems
• On the collision local time of sub-fractional Brownian motions
• A functional CLT for the occupation time of a state-dependent branching random walk
• Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems
• Number variance from a probabilistic perspective: infinite systems of independent Brownian motions and symmetric \(\alpha\)-stable processes.
• Self-similar stable processes arising from high-density limits of occupation times of particle systems
• A simple construction of the fractional Brownian motion.
• 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
• Weak convergence to fractional brownian motion and to the rosenblatt process
• Limit theorems for the motion of a Poisson system of independent Markovian particles with high density
• Some properties of the sub-fractional Brownian motion
• Occupation time fluctuations in branching systems
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