A fractional Brownian field indexed by L2 and a varying Hurst parameter

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Richard, Alexandre^1,2 

[1] Ecole Cent Paris, Regular team, INRIA Saclay, F-92295 Chatenay Malabry, France

[2] Ecole Cent Paris, Lab MAS, F-92295 Chatenay Malabry, France

关键词: (multi)fractional Brownian motion;    Gaussian fields;    Gaussian measures;    Abstract Wiener Spaces;    Multiparameter and set-indexed processes;    Sample paths properties;   

DOI  :  10.1016/j.spa.2014.11.003

来源: Elsevier

【 摘 要 】

Using structures of Abstract Wiener Spaces, we define a fractional Brownian field indexed by a product space (0, 1/2] x 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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free