2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99995We study optimal approximation of stochastic processes by polynomial splines with free knots. 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 we determine the asymptotic behavior of the average $L_p$-distance to the splines spaces, as the (expected) number $k$ of free knots tends to infinity.23 pagesProbability65C30, 60G99 (Primary) 41A15 (Secondary)text