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Quasi-sure functional limit theorem for increments of a fractional Brownian sheet in Hölder norm. (English) Zbl 1338.60087

Summary: In this paper, we investigate the quasi-sure large deviation for increments of a fractional Brownian sheet with Hurst index \((0 < H_1 \leqslant \dfrac{1}{2}, 0 < H_2 \leqslant \dfrac{1}{2})\) in Hölder norm on the rectangles. The quasi-sure set of limit points for increments of a fractional Brownian sheet is also established.

MSC:

60F10 Large deviations
60F15 Strong limit theorems
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[1] DOI: 10.1016/0304-4149(92)90033-M · Zbl 0757.60014 · doi:10.1016/0304-4149(92)90033-M
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