ON CONVERGENCE OF THE UNIFORM NORMS FOR GAUSSIAN PROCESSES AND LINEAR APPROXIMATION PROBLEMS

By Jürg Hüsler, V. Piterbarg, O. Seleznjev. 2003

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Discretization of Stationary Solutions of Stochastic Systems Driven by Fractional Brownian Motion (2009, background): “Define X = (Xt )t∈[0,1] as the piecewise linear interpolation of X with stepsize � = 1/N . Theorem 5 in [ 5 ] now implies that”
A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion (2010, background): “Now let us recall the following result of [14]:”
On asymptotic constants in the theory of extremes for Gaussian processes (2012, background): “[24], Seleznjev [31] for general results on interpolation approximations for Gaussian processes (which is different but related).”
Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion (2006, background): “In [10], in particular the approximation of fBm by its piecewise linear interpolation is studied.”