Free-knot spline approximation of stochastic processes (Q2465309)

Optimal approximation of stochastic processes by polynomial splines with free knots is studied. The number of free knots is either a priori fixed or may depend on the particular trajectory. For the \(s\)-fold integrated Wiener process as well as for scalar diffusion processes the authors determine the asymptotic behavior of the average \(L_p\)-distance to the spline spaces, as the (expected) number of free knots tends to infinity. The theorems are well-formulated and the paper is well-organized.