Spline approximation of a random process with singularity

Konrad Abramowicz, Oleg Seleznjev

Let a continuous random process $X$ defined on $[0,1]$ be $(m+\beta )$-smooth, $0\le m,0<\beta \le 1$, in quadratic mean for all $t>0$ and have an isolated singularity point at $t=0$. In ad…