Optimal series representation of fractional Brownian sheets

By Thomas Kühn, W. Linde. 2002

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Asymptotic Properties and Hausdorff Dimensions of Fractional Brownian Sheets (2005, background): “BelinskiandLinde[6] give a different proof of the small ball probability result of Mason and Shi [25] and have also obtained a sharp estimate for the small ball probability in the case of N = 2 and H1 = H2. More generally, by using different kinds of s-numbers Kuhn and Linde [ 21 ] have determined t”
Sample Path Properties of Anisotropic Gaussian Random Fields (2009, background): “As examples, Linde [64] showed that the integral operators related to fractional Brownian motion and fractional Brownian sheets are strongly locally nondeterministic in his sense.”
Rate Optimality of Wavelet Series Approximations of Fractional Brownian Motion (2003, background): “Kuhn and Linde [ 5 ] have recently shown that there are constants 0 5 ], we say that a representation BH (t, ω) = � ∞=0 Uk(t)� k(ω) is optimal if Relation (1.6) holds.”
Geometric Properties of Fractional Brownian Sheets (2007, background): “For example, Dunker (2000), Mason and Shi (2001), Belinski and Linde (2002), Kühn and Linde (2002) studied the small ball probabilities of an (N, 1)-fractional Brownian sheet BH0 .”