Let Lq,μ​, 1≤q≤∞, denotes the weighted Lq​ space of
functions on the unit ball Bd with respect to weight
(1−∥x∥22​)μ−21​,μ≥0, and let W2,μr​ be the weighted
Sobolev space on Bd with a Gaussian measure ν. We investigate the
probabilistic linear (n,δ)-widths
λn,δ​(W2,μr​,ν,Lq,μ​) and the p-average linear
n-widths
λn(a)​(W2,μr​,μ,Lq,μ​)p​, and obtain their asymptotic
orders for all 1≤q≤∞ and 0<p<∞