L. Plaskota, K. Ritter, and G.W. Wasilkowski

Optimal designs for weighted approximation and integration of stochastic processes on $[0,\infty)$.

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Abstract.   We study minimal errors and optimal designs for weighted $L_2$-approximation and weighted integration of Gaussian stochastic processes $X$ defined on the half-line $[0,\infty)$. Under some regularity conditions, we obtain sharp bounds for the minimal errors for approximation and upper bounds for the minimal errors for integration. The upper bounds are proven constructively for approximation and non-constructively for integration. For integration of the $r$-fold integrated Brownian motion, the upper bound is proven constructively and we have a matching lower bound.

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