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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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