Filtered Brownian motions as weak limit of filtered Poisson processes

DOI10.3150/bj/1116340295zbMath1080.60013OpenAlexW2084055948MaRDI QIDQ1781188

Nicolas Savy, Laurent Decreusefond

Publication date: 23 June 2005

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3150/bj/1116340295

zbMATH Keywords

weak convergencefractional Brownian motionHilbert space valued semimartingales

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Brownian motion (60J65) Generalizations of martingales (60G48) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Cites Work

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• On fractional Brownian processes
• Abstract nonlinear filtering theory in the presence of fractional Brownian motion
• Strong approximation of fractional Brownian motion by moving averages of simple random walks.
• Radonification of cylindrical semimartingales on Hilbert spaces
• CONVERGENCE OF THE WEIERSTRASS-MANDELBROT PROCESS TO FRACTIONAL BROWNIAN MOTION
• The central limit theorem for the Poisson shot-noise process
• RADONIFICATION OF CYLINDRICAL SEMIMARTINGALES BY A SINGLE HILBERT–SCHMIDT OPERATOR

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