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- W2950706695 abstract "Using structures of Abstract Wiener Spaces, we define a fractional Brownian field indexed by a product space $(0,1/2] times L^2(T,m)$, $(T,m)$ a separable measure space, where the first coordinate corresponds to the Hurst parameter of fractional Brownian motion. This field encompasses a large class of existing fractional Brownian processes, such as Levy fractional Brownian motions and multiparameter fractional Brownian motions, and provides a setup for new ones. We prove that it has satisfactory incremental variance in both coordinates and derive certain continuity and Holder regularity properties in relation with metric entropy. Also, a sharp estimate of the small ball probabilities is provided, generalizing a result on Levy fractional Brownian motion. Then, we apply these general results to multiparameter and set-indexed processes, proving the existence of processes with prescribed local Holder regularity on general indexing collections." @default.
- W2950706695 created "2019-06-27" @default.
- W2950706695 creator A5022166266 @default.
- W2950706695 date "2013-12-20" @default.
- W2950706695 modified "2023-09-27" @default.
- W2950706695 title "A fractional Brownian field indexed by $L^2$ and a varying Hurst parameter" @default.
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