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Consistent estimation in partially observed random walks. (English) Zbl 0588.62058
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.
Reviewer: R.Mnatsakanov

62G05 Nonparametric estimation
62G99 Nonparametric inference
62M05 Markov processes: estimation; hidden Markov models
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