Let (Xt)t⩾0 be a Feller process generated by a pseudo-differential operator whose symbol satisfies ‖p(⋅,ξ)‖∞⩽c(1+|ξ|2) and p(⋅,0)≡0. We prove that, for a large class of examples, the Hausdorff dimension of the set {Xt:t∈E} for any analytic set E⊂[0,∞) is almost surely...