Consistent estimation in partially observed random walks (Q1073497)

Let \(X_ 1,...,X_ n\) be independent and identically distributed according to a d.f. F with all central moments being finite and \(N_ i,\quad i=1,2,..\). be a strictly increasing sequence of nonnegative integers. The problem of consistent estimation of the moments of F based only on the knowledge of the sequence \(S_{N_ i}=X_ 1+...+X_{N_ i},\quad i=1,2,..\). is considered. The continuous-time analogue of this problem, i.e. when \(X_ t,\quad t\geq 0\) is a process with stationary and independent increments, is also discussed.