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A fractional Brownian field. (Drap brownien fractionnaire.) (French. Abridged English version) Zbl 0945.60047
Generalizing the approach of B. B. Mandelbrot and J. W. Van Ness [SIAM Rev. 10, 422-437 (1968; Zbl 0179.47801)] to the fractional Brownian motion, the authors define a fractional Brownian field as an \((\alpha,\beta)\)-fractional integral of a white noise measure, with the parameters \(\alpha,\beta\in (0,1)\). The trajectories of the fractional Brownian field are proved to be Hölder continuous, and the field is uniformly continuous with respect to the parameters \((\alpha,\beta)\). The main mathematical tools used within this study are a lemma of Kolmogorov, Borel’s inequality, and many finite increment formulas together with the Lebesgue convergence theorem.

MSC:
60G60 Random fields
60J65 Brownian motion
60B10 Convergence of probability measures
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